Isaac blesses Jacob (Genesis 27), by Govert Flinck, c. 1634
Question: "Can a laymen give a blessing?"
In the absence of a priest or bishop, a layman can give blessings. You can bless your food, for example. You do this by saying the prayer before the meal, and then by making the sign of the Cross over your food. If you are eating with your family, or other Orthodox Christians, this would be done by the most senior person.
It is a pious practice for Orthodox parents to bless their children, at the end of the day, and when sending them off.
If you use a home censer, when you put incense into the censer, you can also bless it.
But just as a priest does not give blessings when a bishop is present, deferring to him, likewise, laity do not give these blessings when a priest or a bishop is present.
A laymen simply forms his hand the same way he does when he blesses himself, but makes the sign of the Cross over the person or thing that he is blessing, and because he is blessing outwardly from himself, He makes the Cross from the top to the bottom and then from his own left to his right (which, when blessing a person, results in the Cross being made over them the same way they would have made it over themselves).
Fr. Athanasios Haros talks about this in the following video:
The only thing I would point out that when Russians give a blessing, they do not make the tiny crosses that he does in this video. Usually (at least as I have observed) they would trace the sign of the Cross over another person just as large as they would do so over themselves.