Is it possible in modern biology to make any person's identical twin (or genetical clone) using his DNA?
I will assume that by "identical twin", you refer to "clones". Individuals who share the same genetics but of course do not necessarily share the same womb. I won't pay much attention in detail epigenetic modification nor in the length of telomeres.

While it has never been done for ethical reasons, we would probably be quite able to make a clone of a human being. We can take a cell from an individual, make it totipotent again, like a zygote and then, insert this zygote into a woman's uterus. The resulting individual is a clone and therefore have identical genetics, just like two identical twins. Similar technics have been used to clone Dolly the sheep.

We cannot, however, modify the DNA in all cells of a living individual to make this individual a perfect cone of another one.