Download and print an IPA symbols chart from the link listed under "Resources" if you don't already have one. Familiarize yourself with the sounds the symbols represented by pronouncing the words underneath them. The "schwa", for example, represents a nasal "a" sound, such as in the word "America."
Make lists of several words from your own language--10 is a good number to start with--which contain sounds each symbol represents. The "schwa", for instance, is present in all of the following English words: about; taken; pencil; eloquent; supply; supple; dinner; seldom; doctor; alarm. Making such lists will not only give you additional real-world context for the symbols, but will also introduce you to the various ways you can use them. Do the same in the language you're trying to learn for additional practice.
Practice transcribing words, phrases and sentences you know into phonetic transcription, making sure to check your answers with a dictionary only when you've completed the transcriptions to the best of your ability. Learning IPA in the context of words you already know will better equip you for reading words you've never seen.
Incorporate new words into your spoken vocabulary by reading their IPA pronunciations from the dictionary. Test your skill at reading IPA by gauging the response you receive when you say the words to others. If they understand the words perfectly, it means you've pronounced them almost or totally correctly--and that the work you've done to master reading phonetic transcription has paid off.