The previous post deals with language learning in general. For some languages, though, you will need to learn a new alphabet as well as the new vocabulary and grammar. Here are some tips I have found useful for learning new alphabets.
First, copy the new alphabet 20-30 times, saying the name or sound of each letter as you do so.
Next, practice writing words using the new letters. Often it is helpful to try writing your name, the names of friends and family members, and miscellenaeous English words, coming as close as you can to representing them with the sounds available in the new language. The point of this exercise is, first, to help fix the shape-sound associations in your head. It will also get you used to forming the new letters. Introductory textbooks of languages with non-Roman alphabets will often have lists of actual words of the language written in its script. Practice copying these, too.
After you have spent a couple of hours doing the above, you will be well on your way toward reading and writing the new alphabet.
Different alphabets present different challenges. If the alphabet is relatively close to Roman (e.g., Greek or Russian), the main challenge will be not to confuse letters of similar or identical shape but very different sound. For example, the English letter "P" is the same shape as the letter for the sound "r" in Greek and Russian. Don't be too frustrated if you find yourself confusing them at first. After a few weeks or months, the new shape-sound associations will be second nature.
Alphabets that are very different from Roman present the problem of a large number of new and different shapes. It will take you longer to learn to distinguish all the letters and associate them with their sounds. For alphabets like this (e.g., Hindi, Arabic, Malayalam), you may find it helpful to make it your goal to learn five new letters a day, rather than the whole batch at once. I still recommend the first step above to begin with (copying the whole alphabet multiple times, etc.). But after that, just expect yourself to learn a few letters each day. This will give you an achievable goal.
Some alphabets, such as Arabic, have groups letters that are made up of the same basic shape with minor variations (in the case of Arabic, varying numbers of dots above or below the same shape). If this is the case, learn the letters in groups. Otherwise, just learn a few letters at a time in the traditional order of the alphabet. A good textbook will divide the alphabet up in a convenient order for learning. It will sometimes spread the alphabet over several lessons, teaching you new words in each lesson that incorporate the letters learned so far. If you have such a book, your task will be made easier.
Above all, persevere! Practice makes perfect, even with complex alphabets. It was months before I finally stopped confusing some of the letters of the Arabic alphabet distinguished only by dots, but I just kept at it and now, years later, I read it without even thinking about it. The secret is to just keep at it.