Praise be to Allah.
Dhikr after Salah (prayer)
The dhikr after salah referred to in the question has been reported in a hadith reported by Abu Hurayrah from the Messenger of Allah (peace and blessings of Allah be upon him): “Whoever glorifies Allah (says Subhan Allah ) thirty-three times immediately after each prayer, and praises Allah (says Al-hamdu Lillah) thirty-three times, and magnifies Allah (says Allahu akbar) thirty-three times, this makes ninety-nine, then to complete one hundred says La ilaha ill-Allah wahdahu la sharika lahu, lahul-mulk wa lahul-hamd wa huwa ‘ala kulli shayin qadir (There is no god except Allah Alone, with no partner, His is the power and His is the praise, and He is Able to do all things) his sins will be forgiven even if they are like the foam of the sea.” (Reported by Muslim, 939).
A number of different descriptions of the dhikr after salah have been narrated, an example of which has been referred to in the question. The evidence for this is the hadith of Abd-Allah ibn Amr (may Allah be pleased with him) who said: The Messenger of Allah (peace and blessings of Allah be upon him) said: There are two qualities, no Muslim man acquires them but he will enter Paradise, and they are simple and easy. He should glorify Allah (say Subhan Allah) ten times immediately after each prayer, and praise Him (say Al-hamdu Lillah) ten times and magnify Him (say Allahu akbar) ten times. I saw the Messenger of Allah (peace and blessings of Allah be upon him) counting this on his fingers. He said: That makes one hundred and fifty on the tongue, and one thousand five hundred (hasanat) in the scales.
[Translator's note: each of three phrases repeated ten times makes thirty; multiplied by the number of daily prayers, which is five, makes one hundred and fifty. Each of these good deeds of the tongue will be rewarded with ten hasanat which will be added to the total of good deeds to be weighed in the balance or scales on the Day of Judgement]. When you go to bed, glorify Him and praise Him and magnify Him one hundred times: that will be one hundred on the tongue and a thousand in the scales. Who among you does two thousand and five hundred sayyiat (bad deeds) in one day? They said: How could we not count (our sins)? He said: The Shaytan comes to any one of you whilst he is praying and says, Remember this, remember that, until he finishes his prayer and does not do (this dhikr), or he comes to him when he is lying down and makes him sleepy, until he falls asleep (without doing this dhikr). (Abu ‘Isa said: This is a hasan sahih hadith. Sunan al-Tirmidhi, 3332).
Dhkir before sleeping
Among the adhkar that may be recited before going to sleep, as referred to in the question, is that reported in the hadith of ‘Ali ibn Abi Talib (may Allah be pleased with him), who said that Fatimah (upon whom be peace) came to the Prophet (peace and blessings of Allah be upon him) and asked him for a servant. He said, “Shall I not tell you of something that is better for you than that? When you go to sleep, say Subhan Allah thirty-three times, Al-hamdu Lillah thirty-three times, and Allahu akbar thirty four times.” (Reported by al-Bukhari, 4943)
How to count tasbih with fingers
As regards counting this tasbih , the Sunnah is to use the fingers of the right hand, although it is permitted to use the left hand. The evidence that the right hand is preferable was reported by Abu Dawud (may Allah have mercy on him), who said: ‘Ubayd-Allah ibn ‘Umar ibn Maysarah and Muhammad ibn Qudamah, among others, told us: Aththam told us from al-A’mash from ‘Ata ibn al-Saib from his father from Abd-Allah ibn ‘Amr who said: I saw the Messenger of Allah (peace and blessings of Allah be upon him) counting the tasbih. Ibn Qudamah said: With his right hand. (Sunan Abi Dawud, Kitab al-Salah, Bab al-Tasbih bil-hasa)
It was said in Hashiyat at-Tahtawi: “It is correct that he (peace and blessings of Allah be upon him) used to count the tasbih on his right hand. It was reported that he said: Count with your finger tips, for they will be asked and they will be made to speak. Ibn Hijr said: Counting the tasbih with the fingertips is better than using the subhah (prayer-beads or rosary).”
The sunnah is to count with the fingertips by putting them on the palm of the hand. As to precisely which finger of the right hand one should start with, I have no specific information on this.
And Allah knows best.