One of my friends graduated from Anna University. According to him, you must have the following documents if you want to get the transcripts,

• 1 copy of your 10(+2) board exam certificate and class 10 board exam certificate for proof of date of birth.
• One copy of ID proof.
• One demand draft in favor of the “Controller of Admissions, Anna University, Chennai – 600025” for the amount of Rs 750 for n where ‘n’ is the number of copies you want. 
• If you do not know how to get a demand draft, ask for one at your bank. They will get you a demand draft.
• One passport-size photo.
• If you have got your degree, get photocopies of the degree. If you want one transcript then one photocopy of the degree would be enough to get them as per your wishes. 
• You can use your provisional certificate if you have not got the degree yet.
• One copy of your consolidated marksheet is the single sheet that will have all the marks you have obtained from all your semesters. Only those who have not got their consolidated marksheet can use their individual mark sheets for the semesters.
• One A4 size courier cover.

If someone else is collecting your transcripts, you have to write a letter that gives this person the authority along with a valid ID proof with them.

After you have got everything, go to the Transcript Department of Anna University. You will get a form there. After filling and submitting the same, wait for a couple of hours. 

After you have submitted, you may get a letter or an SMS once the transcripts are ready. You may also not end up getting notified so remember what their contact number is. The process takes about 10-15 working days.