Normally skins will have a Download link, super old skins may have broken or no longer available download links.
Once you do find one to Download, simply drag the .osk file onto your client, or simply double click or run the file. (only need to click once from Browser menu)
If the double click option doesn't work, it may be because osu! isn't set to open that file, and you'll need to change that by right clicking, Open with, Make sure Always use this program is selected, and Select osu! if osu! isn't there, you will need to hit Browse, and locate the osu! exe manually. The default install path is appdata/local/osu!
You will most likely not need do this though.