The formal ritual of Saranagati or Prapatti is a Vedic and Puranic, scriptural and tradition backed ritual called Pancha-Samskara or "the five impressions" and another name is Samashrayanam. The individual receives the following:
An initiation 'spiritual' name such as a name of Vishnu or one of his devotees such as Ramanujacharya, suffixed with the worddasa. Examples being Vishnu dasa, or Ramanuja dasa.
Tiruman or Tilaka on the forehead and 12 marks on certain parts of the body, which signifies that they belong to Vishnu and that their bodies, minds and Souls is the walking temple of Laxshmi-Narayana.
Special branding on the shoulders of the Conch and Chakra or wheel of Vishnu by the guru.
O Lord, I do not know Dharma, I do not know Dnyana, I do not have Bhakti in your divine Lotus Feet. All I have is I am Akinchan, and Ananyagati. This akinchan and ananyagati soul is surrendered to your Lotus Feet.
In Sri Bhagavadgeeta Bhagawan Sri Krishna explains Saranagati to Arjuna after explaining in detail Karma, Dnyana, Bhakti Yogas. Sri Bhagawadgeeta is a saar of all the vedas, upanishads, puranas. And The following shloka is a saar of Sri Bhagawadgeeta. This shloka being Saranagathi mantram offered by Lord Sri Krishna to Arjuna, it is regarded as one of the three divine mantras of Srivaishnavism. It is also called as Charam Mantra
Sarva Dharmaan Parityajya Mamekam Sharanam Vraja|
Aham tva sarva papebhyo moksha ishyami ma shuchaha||
O Arjun, you relinquish all dharmas and surrender unto me. I shall deliver you from all the sins. Grieve not!
Dharmo Me Sadhan Bhava Taji Kainkarya Ki Kari Bhavana
Muzako Hi Sadhan Maani Raho Yadi Param Pad Hai Pavana
Mat Prapti Pratibandhak Agho Se Avashi Tohi Chhudavunga
Mati Shoch Nischaya Parampadmein bhi tumhe pachuchavunga
Leave sadhan bhav in all the dharma or activities and treat them as bhagavad kainkarya received from Bhagawan. You treat Only ME as your Sadhan if you want to attain Param Padam. I will release you from everything that obstructs you from attaining ME. Do not worry I Shall even carry you to the Param Pad Dham. Although often used interchangeably in common parlance, Saranagati is different from Prapatti. Saranagati refers to the seeking of God as the ultimate means for liberation, whereas Prapatti is the surrender of one's ego to receive the grace of God. The surrender of one's ego through Prapatti leads to the opening up of the grace of God whereas the invocation of the always freely available grace of God through prayer disarms one's resistance to goodness. Charama Sloka describes Saranagati whereas the fourth injunction of Shri Krishna "Ma Namaskuru" in the previous verse describes Prapatti. Prapatti is necessary at the end of all yoga practices because all of them boosts the ego by giving Siddhi-s which prevents the merger of the individual consciousness with God consciousness. Renunciation of Siddhi-s leads to Kaivalyam, that is, Liberation. When Arjuna surrendered to Shri Krishna at the beginning of the Bhagavad Gita partly because of weakness, there was not much merit to deserve anything in return other than the teaching that would empower him, whereas after hearing the teaching and after practicing the yoga to fulfill his responsibilities that would earn him security, wealth, fame etc., he could offer something to receive the grace. However, since it is almost always practically impossible to practice Yoga well enough to become perfect in one lifetime because of the sinful tendencies accumulated over countless births, sufferings that are endemic in this world, and temptations that always distracts one from the path, and since it is difficult for a great personality like Arjuna to be humble, Shri Krishna offers unconditionally the ultimate option of Saranagati for release, which is the dependence on Him, Who is an infinite ocean of love, omnipotent and infallible.
In practice
In Sri Vaisnava Tradition Saranagati is divided into six divisions:
Accepting those things that are favorable for devotion to God
Rejecting those things that are averse to surrender to God
Considering God to be one's protector in all circumstances
Accepting God as one's maintainer
Surrendering everything in God's service
Cultivating a humble attitude
In Goudiya Tradition Saranagati is Divided into ten Parts
Dainya
Atma Nivedana
Goptritve Varana
Avasya Raksibe Krsna Visvasa Palana
Bhakti Anukula Matra Karyera Svikara
Bhakti Pratikula Bhava Varjanangikara
Bhajan Lalasa
Siddhi Lalasa
Vijnapti
Sri Nama Mahatmya
In ultimate vaishnavism sampradhya the nutshell is Saranagathi has 6 elements -5 angas & an angi
acknowledging ones helplessness
determination not to err again
vowing to follow rules
unshakeable faith that the Lord is the sole refuge
seeking the lord as protector
These are 5 angas
surrender itself in accordance with 5 angas is called angi
Reference:The Hindu newspaper dated january08-Sunday-2017SpcialIssue vaikunta ekadasi
