How can I go about developing my ability to taste flavors in coffee?

There are several approaches that can aid in developing your palate.

Cupping

The preferred method of tasting coffee. This requires only a cupping bowl and spoon. Dose out coffee, pour in the hot water evenly, and at 4 minutes skim off the top to remove the crust while carefully not disturbing what has settled at the bottom. Wait about 12-14 minutes for the coffee to cool to a desirable drinking temperature, and slurp the coffee with the spoon.

Types of flavors

There's a variety of descriptions you can use to describe the coffee. Try describe everything. The mouth feel: is it full bodied or light? The acidity: Is it citric or stone fruit? The Smell: What are the aromatics?

Note keeping

Every time you taste coffee, keep notes of what flavors you taste. Basic notes of chocolate or smoke are fine, more nuanced flavors like cherry or plum may come out. Don't be afraid to write exactly what comes to mind. If the coffee tastes like captain crunch then write it!

Comparing coffee

Don't just taste your coffee by itself. Compare it to other roasts you've done. Compare it to coffees from other cafes as well. Note the differences.

I would (with some bias) highly suggest reviewing all of the coffee you drink using Gastrograph Review for iOS or Android.

This will help you directly address the problems you state in your question:

1. It will help you better resolve specific flavors
2. It will help you learn to differentiate specific regions and processing methods
3. It will help you understand you preferences (the flavors you like or dislike)
4. It will keep a log of all the coffee you drink and enjoy

You can see a tutorial for how to review here.