Most Greek letters have striking similarities with Latin characters in terms of pronunciation, so it would be useful if you memorized them along with their similar counterparts. For example, "p" produces the same sound as "π" and "t" is similar to "τ." However, some letters produce distinct sounds, such as "Γ" which resembles "gh," or the Latin "W" which can only be written as "ο..." in most cases.
You can find each Greek letter's traditional transliteration at the Greek Language and Linguistics website (See Resources).
Link every Greek Letter with an easy-to-remember word, containing the letter's sound. The Greek Language and Linguistics website contains examples of each letter's pronunciation, but you can also try to find words yourself. It's a more efficient --- and fun --- way to memorize the alphabet. For example, "A" as in After, "B" as in Vote, "Γ" as in Yarn, """ as in THat, "Ε" as in Elf, "--" as in "Zodiac" and so forth.
A fun way to learn the letters of the Greek alphabet is to memorize Keith Petrower's song. You can find the song at iCompositions, along with its lyrics (See Resources). The artist's pronunciation is not perfect, but the song gives you the opportunity to learn their Greek letters at their proper position. This is a similar method to how students of elementary schools in Greece memorize their alphabet, without the use of the piano and extra English lyrics, of course.
To write Greek letters, you only need to draw a few lines. Most letters can be formed with one quick move, but as a novice, you need to learn writing each letter step by step. The NT Greek website offers a comprehensive guide on how to form both capital and small letters (See Resources). You don't have to follow the instructions if have figured out another way, provided of course that the result is the same.