If it's Chrome/Firefox, just use the "Network tab" in Developer Tools.
If you don't want to use that, try Fiddler, as it automatically proxies browser traffic.
If it's an application, use Microsoft Network Monitor, as it will let you filter packets by process.
If the application uses SSL(i.e. HTTPS), use a combination of ProxyCap/Proxifier + Fiddler to see contents of the encrypted traffic.