Obtain and study a chart that compares the cursive letters, both upper and lowercase, with their corresponding printed letters. You can easily find one of these charts online, or in many English language and penmanship books.
Use flashcards to learn the cursive alphabet. Study the cards independently as long as you need to until you feel comfortable recognizing letters by shape.
Ask someone to quiz you by holding up a card and having you name the letter on the front. Working with the cards repeatedly will help you learn the cursive alphabet on sight, and will help you keep the letters in your permanent memory.
Use cursive writing worksheets that show the proper strokes for each letter to help you practice. As you form each letter, repeat the letter's name aloud to yourself to reinforce memorization.
Practice reading cursive. Even when you're not sure of every letter, oftentimes you'll be able to figure out the word from the letters you do know. The more you read cursive writing, the more easily you'll be able to identify each letter.