Four ways:
1. RemoteJoyLite - Video quality is terrible and your frame rate will be much worse for most games.
2. Emulation via JPCSP or PPSSPP - Poor compatibility and tons of glitches for most games that do work, requires a fast PC, but games can be run at a high resolution.
3. LKV7000 (PSP-to-VGA) - Not that easy to find these days.
4. LKV8000 (PSP-to-HDMI convertor box) using an HDMI-to-DVI cable - Make sure to get the 1080p model if you go this rout, the 720p-only models have lag.