IIRC, you can see some flower fields from the “Oude Lijn” so from trains going between Haarlem and Leiden (which includes some but not all trains between Amsterdam and Rotterdam).
The Keukenhof is a park devoted to tulips and other flowers. It's itself located in this tulip growing area (the Bollenstreek or “bulb region”) so if you don't mind the entrance price, you could go there, see many tulips in the park itself but also in the fields around it. It's open for two months, corresponding approximately to the bloom season but there is often less to see at the very beginning and at the very end of the period so late April is probably the best time. There are busses going there during the season.
Holland.com (in Dutch) also recommends the second half of April and lists three main areas: between Leiden and Den Helder (that's the one I mentioned before), near Enkhuizen, and finally Flevoland.
Do realize that most photographs deliberately make it all look bigger and more dramatic than it really is. As you can see on your aerial picture, many flower fields are relatively small and lie between buildings, roads and other cultures (or at least non-blooming flowers). The colors are altered too (see comment).