Setting up a proxy in the browser is easier than it seems. In Chrome and Firefox it is done through system network settings: Start → Settings → Network → Proxy. Enter address and port — all browser traffic goes through the proxy.
For working with different proxies, extensions are more convenient — SwitchyOmega for Chrome or FoxyProxy for Firefox. They store several profiles and switch with one click. Handy when you need different countries or types.
Important: the system proxy applies to the whole browser, including banking tabs. An extension applies only to chosen profiles. For work, the second option is better.
Checking that the browser proxy works is simple: open any IP-check site — you will see the proxy address and its country. If you see your own IP — the setting did not apply.