Starting up a radio station can be quite expensive or extremely cheap, depending upon what sort of station you're interested in setting up. Internet stations can cost next to nothing, whereas you need deep pockets to set up a new commercial station.
Decide whether you want to set up an amateur or commercial radio station, and whether you want to broadcast it over the Internet or AM or FM radio. Broadcasting over radio frequencies will require a government license (from the Federal Communications Commission the US) and commercial, high-power radio licenses can sometimes be difficult and expensive to acquire. Broadcasting over the Internet will certainly be the least expensive option.
Choose the type of music you will want to be and decide how large of a music collection you will need. If you are simply playing the current top singles, you will not need a large collection, whereas if you're catering to a niche like jazz or soul, you may need several thousand songs. Add the cost of acquiring copies of these songs.
Add up your equipment costs. This is highly dependent on the broadcasting method you choose. High-power commercial setups can easily run upwards of tens of thousands of dollars, whereas a used, low-power setup can be cobbled together for significantly less, particularly if you already have knowledge of radio electronics. Internet stations will require a dedicated computer and specialized software.
Factor in the cost of providing a space for your station. Radio stations may be subject to licensing requirements and building codes, whereas Internet stations can be run from home quite easily.
Calculate the operating costs of your station. For radio stations, this will include building and electricity costs, as well as equipment maintenance and any personnel you need to hire. For Internet stations, you will need to determine the cost of bandwidth, which will be dependent on the size of your audience. There are a number of bandwidth providers that cater specifically to Internet radio.
Determine the music licensing costs. Unless a song has an open license, you will have to pay a fee every time you want to play it on your radio station. If you are a commercial station, this can be fairly expensive; however, local and Internet radio stations are often able to take advantage of special deals by joining certain organizations. Consult your local radio associations for details.
Choose whether you want to spend any money on publicity. If you're a commercial station selling advertisement, you will almost certainly want to take advantage of the public interest generated by your opening.