Unfortunately, you cannot buy or trade a House Elf - they stay with the same families for generations. If you keep your eyes open you may be able to find one who has been freed by their family, although these elves are usually distraught and too depressed to work.
no but a free elf
There is a House Elf and his name is Dobby.
Dobby is a house elf. They serve wizarding families like slaves and can only be freed if they are presented with any type of clothing by their master.
The house elf has a full set of fingers and toes.
The reward for Dobby the house elf was a sock. Chamber of Secrets by J.K Rowling