Do you want to build a transmitter yourself ? That is not legal.
There are frequencies that are legal to use with low power. The frequencies depend on the country you live in.
If you know more or less what you want, you can buy a module for transmitting and receiving.
Have a look at this page, it shows what is possible with the Arduino : https://www.sparkfun.com/categories/16?sort_by=price_asc&per_page=200