How to learn the Tamil Alphabet

Learning a new orthography can be intimidating, but it is not really that difficult if you know how to start.

A little background:
Tamil is technically an abugida, which means that the letters are based on syllables, they contain (usually) both a vowel and a consonant and each change of consonant follows a predictable pattern. Looking at a Tamil க(ka) and கி(ki) you see a hook added to make the "i."

Online Sources for Learning the Tamil Alphabet

• A B C of Tamil [pdf] Short book from Tamil Virtual University which introduces the alphabet and moves on to basic grammar
• Basic Tamil ebook [pdf] also from Tamil Virtual University. Workbook for alphabet.
• Tamil Script Learner book from a professor at The University of Texas at Austin.

As for learning these new letters...
Start with an alphabet chart, and a couple of words you are learning. Start with maybe 5-10 words. You might start with the Alphabet learning workbook from Tamil Virtual University.  You can also jump straight into the Duke University web lessons, and slowly match up the letters in an alphabet chart. Basically you want to pick a few words, and practice the letters in those words. Practice the letters separately, copying them out, for example:
அ அ அ அ அ அ அ
ம் ம் ம் ம் ம் ம் ம் 
and also within words. அம்மா (mother), ஆமாம் (yes) , மாமா (uncle)

You can use any vocabulary list to start learning the alphabet. I don't recommend making flashcards for all 247 letters. I think it is a better usage of your time to focus on words that are currently in lessons you are working on, and then you will find yourself recognizing and knowing letters that you may not have explicitly practiced.

It is also useful to use Azhagi, NHM or the google transliteration for copying Tamil texts. You can immediately see if you are associating the correct sounds with the letter. Find texts in Tamil, and copy them again into your word processor/email or blog. 

More simple sentences, plus some adjective work

These sentences and phrases come from the Intermediate Textbook made available by the Tamil Virtual University.
This is from Section 3 of Unit 1. Unit 1 spans 20 pages, some are sample sentences, others are  worksheets. I won't recreate everything here, but instead focus on translations and vocabulary.

Section 3
I have color coded each Tamil/English sentence pair since the sentence word order differs.  This also shows you how certain English words are unnecessary or implied in Tamil.

இது சிங்கம், சிங்கம் விளங்குகளில் வலியது.
This is a lion, the lion is strong among the animals.

இது யானை, யானை விலங்குகளில் பெரியது.
This is an elephant, the elephant is big among the animals.

அது மான், மான் சாதுவான விலங்கு.
That is a deer, the deer is a gentle animal.

இது கங்காரு, இது ஒரு ஆஸ்திரேலியா விளங்கு, இது இந்தியக் காடுகளில் இல்லை.
This is a kangaroo, it is an Australian animal, it is not native in the forest in India. (native is my best guess for காடுகளில்)

அது தான் சிட்டுக்குருவி, சிட்டுக்குருவி புறவைகளில்  சிறியது.
That is indeed a sparrow, the sparrow is small among birds.

இது மயில், மயில் ஆழகானது, இது இந்திய தேசியப்பறவை.
This is a peacock, the peacock is beautiful, it is India's national bird.