1. Check the Weather & Flower Forecast
The tulips bloom typically within a set period: late March to early May. It depends on the year, but you're more likely to see tulips in bloom if it's in April. There's quite a few websites that will update in February/March on the season's prediction for blooms for those planning ahead of time.
There is a way to check the flower forecast to find out WHEN and WHERE to go. There's a website called BloemenRadar.com where you can check to see where flowers (not all are tulips) are in bloom within the past week. You can just enjoy the photos OR zoom into a location to find out where you need to go. There's not ONE single location and you can't walk onto ALL of the fields, but it should give an idea of where is a good area to visit.
2. Take the Train to Leiden
You can save money if you can buy a "Dagkaart" from a store, which means you get unlimited travel on a train for the day for a fixed price (usually 16 euros and under). People who don't live in the Netherlands will be unable to buy one online, but if they're being sold in Blokker, Hema, Albert Heijn, Etos, or Kruidvat, you can buy one in cash as long as they don't sell out (OP=OP!). Just be aware that there are typically conditions about traveling after rush hour or only on a weekend and the valid dates, but it's good to check with a clerk at the store about the specific conditions of your card before you buy it. The linked website shows day ticket deals on a monthly basis.
3. Rent a Bike
Just visiting? Sorry, OVFiets is NOT an option. I used EasyFiets for my rental. It was 7.50 euros for the day with a 50 euro deposit for all three bikes after the guy decided we weren't likely to steal the bikes. A pretty good deal for only a ten minute walk from the train station.
A lot of the roads with the tulips are country roads, so watch out for cars/scooters/pedestrians. Not all fields will be accessible as some will have a ditch protecting people from walking onto them, so pick a field close to other blooming ones, just in case your first one fails (like mine). You'll pass through some cute traditional Dutch towns worth enjoying with some traditional architecture.