With fingers or pliers, slightly squeeze the plates together while using thumb and index finger of opposite hand to push the plates in opposing direction. Newer chains, especially if a bit cruddy, can be more troublesome. Placing a small rag between your fingertips and the link may prevent some skin getting pinched.
Buy the tool for $15, it's worth it. Available online of course, and any LBS that has a Park Tool display.
Yes, you can sometimes get it off by hand. I emphasize "sometimes" because you can sometimes spend many, many frustrated minutes not getting it off. You can use a needlenoose pliers if you have one that is thin enough. You can make/grind a tool that will work perfectly. There's many ways of getting it off without the tool, I've used and tried them all.
But for $15 you can buy a tool that is easy, quick and in the coming months and years will be used dozens of times, and might actually make it so easy to remove a chain that you take if off to clean it more often (if that's your thing).