You need a demat account in same name as the share certificate holder to transfer the shares in demat.
So you will need to open a demat in same name as the physical certificate has.
After doing this, you need to fill the dematerialization form and submit the physical certificate to the broker.
This will then be sent to RTA who will verify the signatures and if found correct will then credit the shares into demat account.
Things to look out for:
1. The signatures are correct. Mostly due to passage of time, your signature might change.
2. You have the right certificate - Might be in history the company has issues bonus shares, so you will loose out on those bonus shares if you produce the old certificate.
The time required for this transfer repends on RTA and is usually between 2 weeks to 1 month.