Here's how you can do it:

1. Acquire a copy of <a href="http://www.modchip.com/breakerpro.htm">Breaker Pro</a>. How you get it is up to you, but know that it can be burnt.

2. Use Swap Magic to boot Breaker Pro if it's not legitimate, or just boot an authentic copy.

3. Then use Breaker Pro to boot your PS1 game.

There are other methods you can use, such as a memory card loader (notoriously unreliable and causes an area of undeletable, corrupt data on your memory card) or, of course, a modchip. I eventually got a mod chip because I got sick of having to swap discs all of the time.