Before a proxy will route your traffic it has to know the request is yours. There are two standard methods: username and password credentials, or IP whitelisting. Most modern gateways use credentials, because that's also where your targeting parameters live.
Username and password
You send a login and password with each request (your HTTP client and most tools handle this for you). The gateway authenticates you and routes the traffic. This is the portable method — it works from any machine or server without pre-registering its address.
Crucially, the username is also where targeting goes. Parameters like country, city or a sticky session id are appended to the login, so a single credential can request very different exit IPs depending on what you tack on.
IP whitelisting
Instead of credentials, you register the public IP of the machine making requests; the gateway then trusts any traffic from that address. It's convenient for a fixed server because there's nothing to embed in each request.
The catch is mobility: if your IP changes — a new server, a dynamic home connection — you must update the whitelist first, or you're locked out. For dynamic environments, credentials are simpler.