If you purchase a registered domain name, how to actually transfer the domain ownership from the previous registrant to you? Also, will you have to pay the renewal fee immediately after you buy it?

Whoever owns the domain name has to initiate the transfer process. Most domains require you to have the EPP code (security key) in order to initiate and complete a transfer. Also, make sure the domain is UNLOCKED before the transfer.

Most transfers will also renew your domain name for another year once completed (depends on the registrar).

When you buys domain you shall ask the one who is selling it to move it to account of yours with their current registrar or to authorize a transfer to your registrar.