No country in the world has better cycling infrastructure than the Netherlands (and Denmark). In the Netherlands, the vast majority of motorists are themselves cyclists. The Dutch motorist association, ANWB, started off as a cyclist club, and is still majorly involved in cycling issues. Looking out for cyclists is a prominent part of driver training in the Netherlands.
A wonderful blog in English is Bicycle Dutch. Other than text blog posts, they also make many YouTube videos.
You may find Actueel Hoogtebestand Nederland, an electronic topographical map of the Netherlands, useful. (Yes, the Netherlands has topography. And Dutch people love topographical maps, based on the number of topographical maps and atlases available at bookstores in the Netherlands. Well, I love topographical maps too.)
Dutch people basically always check for possible rain/hail/snow before venturing outside. Check out the websites and apps of these: buienradar.nl, or buienalarm.nl. There is also ventusky.com, which shows weather pattern all around the world.
There are many shops that tourists and other people can hire bicycles from.
One thing that is absent in the Netherlands is city-based road-side automated bicycle rental. But then, that is not really needed in the Netherlands; people already have multiple bicycles parked at various train stations, or they ride their bicycles all the way everywhere, or they have folding bicycles that they take on trains, or something like that.
Even better than the city-based bicycle-sharing systems that is available in other countires, is the national bicycle-sharing system in the Netherlands. OV-fiets is available at more than 270 locations nationwide (most are at train stations). Many of them have huge fleets of bicycles available. There are various types of renting localities; some have an attendant, and some are automated.
Keolis has the KeoBike, currently available in certain parts of Utrecht and Gelderland provinces. These bicycles can be hired through the KeoBike app.
The Hoge Veluwe National Park in Gelderland Province is famours for its white bicycles. The park admission fee includes the usage of the white bicycles. You can ride them freely within the park, and there are bicycle stations at the park entrances and at other key locations within the park (e.g. at the Kröller-Müller Museum) where you can pick one up or leave one behind. (The bicycles cannot be reserved. The entire border of the national park is fenced. The Hoge Veluwe is the only national park in the Netherlands which has an admission fee.)
In Belgium, there is the national bicycle-sharing system called Blue-Bike; they can be found at nearly 50 train stations nationwide. There are also the city-based systems Villo! in Brussels, Velo Antwerpen in Antwerp, and Li Bia Vélo in Namur. In Luxembourg City, there is vel'oh!. There are also many similar city-based systems in Germany and France.
In the Netherlands, bicycle helmets are usually only worn by young children, professional cyclists/handbikers/wheelchair-racers, other sport cyclists like mountainbikers, other 'fast' cyclists, or foreign tourists. (Sorry, I am not trying to discourage you; bicycle helmets save lives. Do wear a helmet if you do not feel safe without one.)
Netherlands has the second best bicycle safety record in Europe after Denmark, in terms of deaths per cycled distance. (But then, Denmark is also much less densely populated than the Netherlands.) Instead of making bicycle helmets compulsory, the Dutch government makes the entire traffic system safer for cyclists. This is a little read (out of many other similar ones on the internet) about the (non-)usage of bicycle helmets in the Netherlands.
Bicycle paths are ubiquitous. Amongst the dense network of bicycle paths is the fietsroutenetwerk 'bicycle route network', a.k.a. fietsknooppuntennetwerk 'bicycle junction network'. Important bicycle path junctions are given numbers, and the junction numbers are signposted along the routes of the network (see examples in the Dutch Wikipedia article, and photos below). The network was first built in northern Belgian Limburg, and now the network covers the entirety of Flanders and European Netherlands. The network extends into some bordering parts of Germany, and parts of Wallonia have joined the Flemish network. (Most prominently, Western part of Hainaut, and the East Cantons (Eupen-Malmédy). Parts of Namur Province and Belgian Luxembourg have little networks that are not yet joined to the main network. See the Dutch Wikipedia article. Brussels-Capital Region does not participate in any of these, and has its own bicycle route network.) Many guidebooks and digitial guides give recommended scenic routes in strings of bicycle path junction numbers. There are numerous websites and apps that show the network, with some also allowing you to draw your own map by clicking/pressing the numbers of the junctions in the order that you want. This is one Dutch example with English, another Dutch example, another Dutch example, and a Belgian example.
Mostly-overlapping with the fietsroutenetwerk is the LF network; LF stands for landelijke fietsroute 'national bicycle route', or lange-afstand fietsroute 'long-distance bicycle route'. The LF network covers the whole European Netherlands and Flanders. The LF routes are signposted like the fietsroutenetwerk. The LF routes are recreation-oriented long distance bicycle routes (i.e. they are not necessarily the most direct route between urban centres). LF is followed by a route number (currently 1 to 51), and then an a or a b, which indicates the direction: a is generally from north to south, or west to east, while b is generally from south to north, or east to west. For instance, LF1 runs roughly along the western coast: LF1a signifies LF1 in the direction from Den Helder (Noord-Holland) in the north, to Boulogne-sur-Mer (France) in the south; LF1b signifies LF1 in the reverse south-to-north direction.
The long-distance bicycle path networks in nearby places are called RV (Rando-Vélo) in Wallonia-Brussels, PC (pistes cyclables) in Luxembourg, and D-Route in Germany.
There are also the fietssnelwegen 'bicycle highways' (in Flanders a.k.a. fietsostrade). In Flanders there is a national system, and the numbering has an F prefix. (But, see this 2014 review of the section of F 1 between Antwerpen and Mechelen.) In the Netherlands, the bicycle highways are not (yet?) so uniformly signposted. Sometimes they have numbering with an F prefix, and the numbering matches that of the car highway parallel to them. For instance, the bicycle highway between Nijverdal and the German border west of Enschede is officially called the F 35, as it parallels the A 35 motorway/N 35 highway (see this 2013 review, before much of it was built). The RijnWaalpad between Arnhem and Nijmegen has the designation F 325 (signs with this designation have appeared most of the way), as it parallels the A 325/N 325 (see my little F 325 page, and also this 2015 review from Bicycle Dutch). See the Dutch Wikipedia article for a list of bicycle highways in the Netherlands and Belgium.
The various bicycle path networks are indicated in many maps. The Cycle Map layer in OpenStreetMap is a useful tool.
(There may be no 'real' mountains, but) Mountain-biking is popular in the Netherlands. The following are some websites which list mountain bike trails: Trails.bike, MTBroutes.nl, Bikespot.nl.
The symbol for mountain-biking is a triangle with two small circles on one of its edges. In the following example, the word vergunning means 'permit'; you need a permit (in this case, from Natuurmonumenten) for mountain-biking here. (Get the permit here.)
Remember that all parts of the Kingdom of the Netherlands, like the rest of Continental Europe, has right-hand traffic; traffic goes on the right hand side of the road/path. (Well, with bicycles, sometimes Dutch people rides creatively.) Here is a brief post on cycling rules and regulations in the Netherlands.
The following are some signs and cycling-related words that you will see in the Netherlands. See also the pages on moped-riding, motorcycling, and driving for more insights on Dutch traffic rules. (The 'sign numbers' mentioned below, e.g. 'sign E2', are their names in Dutch traffic law.).
A mini glossary of 'bicycle' and 'to cycle':
Fietsenstalling is a bicycle parking garage/facility. There are public bicycle garages all around the country, most of them are free. A bewaakte fietsenstalling is one that is watched by an attendant. Typically, when you enter with a bicycle, a ticket is attached to the bicycle, and a corresponding ticket is given to you. You then park your bicycle inside. (You have to use your own bicycle lock.) When you come back to retrieve your bicycle, as you leave the bewaakte fietsenstalling with your bicycle, you have to show the ticket to the attendant, and the attendant will then check whether it matches the ticket attached to the bicycle.
There are other types of bicycle storage facilities. For example, see what NS has to say about the various types of bicycle storage facilities near train stations. (For the NS operated ones, most of them charge a small fee; some require an OV-chipkaart). Some Fietsenstallingen do not allow overnight parking; some allow, but charge an overnight fee. Do not leave valuables with your bicycle. (It is probably not a problem, but) I suggest that you use a heavy-duty bicycle lock, even in a guarded storage facility.
See bicycle carriage rules in the pages for domestic trains, and for international trains. (In Germany, some public transport providers require you to have a bicycle cover.) Carriage of bicycles on buses is generally not allowed in the Netherlands (unlike some buses in nearby Germany), unless it is a folded-up folding bicycle. Try searching for fiets meenemen 'bicycle take-along' (Dutch), Fahrradmitnahme (German) 'bicycle take-along', or emporter vélo à bord 'take bicycle on-board' (French) on the websites of the individual public transport providers.
ANWB, other than providing roadside services for cars, also provides roadside services for bicycles (and also other types of vehicles).
You might also want to consider bicycle insurance, offered by ANWB and many insurance companies. With a huge number of bicycles, the Netherlands also has a problem with bicycle theft. Invest in, or borrow, heavy-duty bicycle lock(s). Make sure that you lock it properly.
Electric bicycles are also popular in the Netherlands. (Being frail or less fit is not an excuse for not cycling in the Netherlands). Public charging stations for electric bicycles are increasing seen. Here is one electronic map of e-bicycle charging spots in the Netherlands, and one in Flanders.
Electric bicycles are considered bicycles, if they are not capable of going faster than 25 km/h. A driver licence is not required for bicycles. (Rijksoverheid says so.)