Learn the 57 symbols of Hindi, which include 40 consonants, 10 vowels, 2 modifiers, and 1 character that used to represent a vowel but is not used anymore, and four conjunct consonants. Learn the sounds that each letter makes, and how to form them
You can learn the various symbols at http://www.avashy.com/hindiscripttutor.htm, which provides an interactive writing tutorial to new learners of written Hindi. You can see animated symbols being written, hear how symbols sound, as well as hear them in the context of Hindi words.
Increase your Hindi vocabulary by taking Hindi lessons. You will begin to recognize words written in the Devanagari script. Pay close attention to words that use matras.
You can take Hindi lessons online by hiring a private tutor or attending online classes. One website that offers Hindi Lessons is HindiLearner.com. Check with local Indian and Hindi heritage and cultural centers to see if they offer Hindi courses in your community.
Read and write in Hindi as much as possible. Focus on words that use matras, and look for patterns in how they are used. Read a variety of texts so that you are exposed to a wide range of vocabulary. You can find some Hindi news texts to practice reading at http://www.bbc.co.uk/hindi/.
Write vowel and consonant combinations repeatedly until they are formed correctly. Write different words that use the same set of consonants and vowels, and then practice writing a new set when you have mastered the previous one.
Practice writing matras by writing at least a few sentences in Hindi every day. Ask a friend who speaks and writes Hindi fluently to correct your sentences and letter formation. Join an online language exchange such as My Language Exchange, and ask your language partner to correct your Hindi writing via e-mail. Scan a picture of your hand writing into your computer, or take a digital photograph of your handwriting, and send it to your partner to correct via e-mail.