Then he should go straight to the Black Stone and facing it make takbir. And he may say `Bismillah' before it - as it is authentically reported from Ibn `Umar, although not from the Prophet.
Then he touches the Black Stone with his hand and kisses it also, and makes sajda upon it also - as the prophet of Allah did that, and `Umar, and Ibn `Abbas. 
If he is not able to kiss it then he touches it with his hand then kisses his hand.
Then if he cannot touch it he should make a sign towards it with his hand.
And he does that in every circuit.
And he should not push and crowd to get to it according to the Prophet's saying: O `Umar, you are a strong man, so do not harm the weak, and when you wish to touch it, then when it become free then touch it, and if not then face it and say takbir. 
And there is in touching the Black Stone a great excellence as the Prophet said: “Allah will raise up the Stone on the Day of Judgement, and will have two eyes with which it will see, and a tongue which it talks with, and it will give witness in favor of everyone who touched it in truth.”  And he said: “Touching the Black Stone and the Yemeni corner removes sins.”  “The Black Stone is from Paradise, and it used to be whiter that snow, but the sins of the idolaters turned it black.” 
Then he should begin making tawaf around the Ka'bah - it being to his left - and he goes around past the Stone seven times - from the Stone to the Stone being one, wearing the ihram under his right armpit and over the left (called l-idteba'a)  throughout the tawaf. And walking quickly and with boldness (ramal - a strong walk in which the shoulders are thrust forwards) in the first three, from the Stone to the Stone - then he walks normally in the rest.
And he touches the Yemeni corner with his hand each time he passes and does not kiss it, and if he is not able to touch it then he should not make any sign towards it with his hand at all.
And he should say between the two corners: “O Allah gives us good in this life, and good in the Hereafter and save us from the Punishment of the Fire.”  Rabbana atina fid-dunya hasanatan wa fil akhirati hasanatan wa qina ‘adhaban nar.
Our Lord! Give us good in this world and good in the Hereafter, and defend us from the torment of the Fire.
[Noble Quran 2:201]
And he does not touch the two shaami corners at all following the Sunnah of the Prophet.