Hello Aspirant, so the procedure of JoSAA ( Joint Seat Allocation Authority) Counseling 2019 is as given below:

Firstly you need to understand that,
•The JEE Main candidates will be eligible to apply for IIITs, NITs, and GFTIs only.
• While JEE Advanced candidates can apply for all Institutes, along with IITs in this counselling.

Also, the seats will be allotted on 3 basis:
1. Merit
2. Preference
3. Category of the candidate

Procedure
So, there will be seven rounds of the Counselling, and the registration for the same will start tentatively from the second week of June 2019.

1. Registration
• You will be able to log into their account, by providing the roll number and password of JEE Main 2019. Your information will be taken from JEE Main database.
• Later you can even change your password as well.
• Also, consider this as a very important step , because without this you won't be able to take part in the counselling.

2. Making Choices
• Now, here you have to choose the Institute and the course in preference.
• A list will also be available, according to your eligibility to get admission (in a particular course/college).
• Lastly, click on 'I agree to lock my choices'.

3. Declaration of Seat allotment
• The allotments will be provided through an online mode by the concerned authorities.

4. Acceptance letter and fee payment on accepting the seat
• You will have to download a provisional allotment letter in this process.
• And make fee payment for seat acceptance
General category- ₹35000
Reserved category- ₹15000

5. Report at the Centres
• You must report at the alloted Centre in order to verify your documents.
• Don't forget to take both the originals and copies.

Documents to be verified
1. Three passport size photographs similar to JEE Main 2019.
2. Provisional seat allotment letter.
3. Candidate Undertaking
4. Proof of fee payment
5. JEE Main 2019 score card
6. JEE Main 2019 Admit card
7. 10th Marksheet/ Date of Birth Proof
8. 12th Marksheet/ Pass certificate
9. Photo Identity Card
10. Medical Certificate
11. Category certificate (if any)
12. PwD certificate (if any)
13. OCI certificate/ PIO card (if any)
14. Print out of filled choices

6. Confirmation of Admission
• You have to visit the allotted college and complete all the necessary documentation, and pay the remaining fee.

All the best!
I hope this helps.