This answer is about the Vadakalai interpretation of Sharanagathi.
Who is considered to be qualified for Sharanagati?
Vedanta Desika answers in the Rahasyatrayasara Chapter 10 (The Fitness for Prapatti)
What is the procedure of Sharanagati?
There are four ways in which Prapatti can be performed. To keep it simple we can consider that there are really two ways: (1) By oneself (if one is qualified) and (2) By seeking someone else.
This 'someone else' is typically an Acharya who knows the Prapatti Prayoga and has attained Siddhi in the three mantras.
The procedure typically involves making a visit to the Acharya where the Acharya makes a formal (ritual) request to the Lord to accept the soul that is performing Sharanagathi. Depending on the specific Acharya the sishya involved may be required to repeat a few Sanskrit phrases that express the feelings of aakinchanya and ananya-gatitva (the concepts described in the above quoted chapter).
Are there any daily practices or rituals to be followed?
Chapters 15-19 in the Rahasyatrayasara describe the life of a Prapanna. In general the goal is to follow as much Varna-ashrama Dharma as possible. I have quoted Chapter 15 below.