Cab won't get you there for $20. It's a lot further than you probably think. You'd be looking at $70-120, depending on where you're going and L.A.'s infamous traffic.

The Valley is a pretty big place. If you tell us where in the Valley you're headed (Chatsworth? Burbank? Sylmar? Woodland Hills? North Hollywood? Van Nuys?), we can probably help you better.

Are you looking for the absolute cheapest even if it's terribly inconvenient (multiple rail/bus transfers?), or would you mind paying a couple dollars more for a little extra convenience?

Cheapest would be utilizing only MTA public transit (either all buses or a mix of Metro and buses), which will cost you $1.25 for each bus or rail line you ride (a $5 day pass isn't a bad idea to keep things simple)--but you're looking at anywhere from 2-3 hours, depending on your final destination.

Depending on where you're going, you may be able to shave off some time by taking the LAX-Union Station FlyAway bus, which runs every half hour (except in the early AM hours, when it's hourly) for $7. You can then take MTA buses/subways for another $1.25 per transfer to get you to your final destination, or, depending on where you're going, Metrolink commuter trains or Amtrak's Pacific Surfliner might speed you to your destination faster ($5-8 for Metrolink or $5.50-12 for Amtrak).

If you're headed to the western parts of the valley, you may be able to take the LAX-Van Nuys FlyAway (also $7) and then catch connecting bus transit from there.

Spendier and more convenient (but horribly uncomfortable) would be one of the airport shared van services. I think a family member once paid $35 (plus tip) from the northwestern part of the valley.

Try pulling up directions on either Google Transit or the MTA's trip planner. Both trip planners may also factor in the FlyAway bus and/or Metrolink commuter train.

You can also reference ToAndFromTheAirport.com's comprehensive collection of information.

Have you considered flying into BUR? Fares into BUR are sometimes the same as to LAX (and occasionally cheaper), and it's right in the Valley, significantly shortening your transit time. It's an option to look into, anyway.