Practice reading texts written in the new alphabet as often as possible. Even if you don't know all the letters or symbols, you will be able to make out some of the words and to guess some of the others. Look out for the names of people and places and for loan-words from your own language as these tend to be relatively easy to spot and decipher.
At first you'll probably find that you have to sound out letters individually before you can decipher the words. Eventually you'll be able to recognise words by their shapes and will only need to sound out the letters of unfamiliar words. You probably went through the same process when learning to read your native language.
Label things around your home or office in the new alphabet with translations in your own language. This will increase your exposure to the new alphabet and help you to recognise key words and phrases.
Try reading aloud whatever material you get hold of. There are links to online newspapers and magazines in many different languages on relevant pages of this site If you know native speaker who is willing to help, ask him or her to read things aloud. Then you try to do the same and ask your friend to correct your mistakes.
