You can't actually hide your IP address — every device online needs one so responses know where to go — but you can replace the one websites see by routing your connection through another server first. A VPN, proxy or Tor all do this in different ways, and each swaps your visible address for someone else's rather than removing it.
VPN: moves your IP, doesn't hide it
A VPN sends your traffic through a server run by the VPN company before it reaches the website you're visiting. Websites then see the VPN server's IP address instead of yours — which is genuinely useful for masking your rough location or getting around IP-based blocking. What it doesn't do is make your traffic anonymous: you've simply moved your trust from your internet provider to the VPN provider, who can, technically, see the same connection your provider used to see. Choosing one means reading what that specific provider promises to log, not assuming "VPN" automatically means private.
Proxy: similar idea, usually less protection
A proxy server works on the same principle — it forwards your request and the website sees the proxy's address instead of yours — but most proxies don't encrypt your traffic the way a VPN does. That means your internet provider, or anyone else on the network path, can often still see what you're doing, even though the website itself can't see your address directly.
Tor: strongest privacy, real trade-offs
Tor routes your connection through three separate volunteer-run relays, encrypting it in layers so that no single relay knows both who you are and what you're visiting. It's the strongest option here for actually resisting tracking, but it's also noticeably slower, and some websites block traffic from known Tor exit nodes entirely.
What none of these actually do
Your browser's private or "incognito" mode does not hide your IP address at all — it only stops your own browser from saving history and cookies locally. Websites see the exact same address whether or not incognito mode is on. And whichever option you use, it's worth remembering it's not eliminating a request for trust — it's redirecting it, from your internet provider to whoever runs the server in between.