You can download apps for your phone (doesnt work on all phones). If it doesnt work you need to connect your phone to your pc and install software to your pc.
Search for "root phone" in google for complete guide or search for apps for rooting.
Samsung Galaxy............you are going to have to be much more specific than that.
There is 8 generations now, with each generation having a good half a dozen variants that can make a very large difference on how (and if) you can root it.
A international version of the phone is quite different software wise than say the Verizon Wireless version.