@OP
Depending on the purpose (the less we know, probably the better), will determine the level of precaution you need to take. If you're wanting to spoof an IP to get around a region restriction on content for example, then a simple proxy would do just fine.
My advice is to search the web for 'IP masking'
You'll find a ton of material on different methods and what they're best for. You'll also get a better answer on the how-to part than we're probably going to allow here, again depending on how crazy this endeavor.
Your asking for advice to hide your IP and that makes me think that you are up to no good,.
Imagine a weekend of gardening planned. You go to the hardware shop and pick up:
- A shovel to dig up the weeds
- A gas can for the mower
- A hack saw to remove the dead branches
- Some rope to tie up dead branches for easy disposal
- large trash bags for misc. shrubbery
- duct tape for a separate project
Should the cashier see your assortment of goods and assume you're planning a murder? I'm suspicious myself, but all things considered, this isn't exactly a request on how to break into a government server.
Some Proxy software: like some program that masks every internet activity. Most effective.
I believe BikerEcho is talking about a VPN service (perhaps?). If so, that's probably your best 'single application' approach. In the study of cyber security, you always take a 'layered' approach... meaning you would do all different things you could (e.g. do all three things in Biker's post and more).
the conversations here need to be really careful.
this