I would say the best method is to let it grow a bit and pull it out so you get the roots or to use a weed spray. If your lawn is mainly crabgrass then you will be left with just dirt and a sore back, so I would start over with new turf.

Thanks Kildermorie. So, with that in mind, if I kill all the grass (and crabgrass) and start over with sod, will the crabgrass come back? Do I need to replace the dirt as well?

Actual crabgrass would have to come back from seed, but it is infamous for that. You don't say where in the States you are, or what kind of grass your lawn is, so it's hard determine the proper way of dealing with it. If your lawn is a rhizomatous perennial grass, such as Kentucky Bluegrass, or Bermudagrass, you could spray the lawn with a strong vinegar solution, about 1/2 cup white vinegar per gallon of water. That would kill all of the leaves, but the lawn grass would come back from the rhizomes. Usually, if you keep the lawn grass healthy, well fed, and well mowed, it has an advantage over the crabgrass, and will crowd it out, eventually.
Clumping grasses, such as Chewings Fescue, Tall Fescue, and Perennial Ryegrass don't have that advantage, and will need to be re-started on clean soil. That means taking a summer to spray the crabgrass, water, and respray the seedlings, until you reduce the seed load in the soil. Many northern and mid latitude grasses prefer to be started in early fall, anyway.
One thing that you may want to check is whether or not it really is crab grass--there are many look-alikes, and many other species that are mistakenly called that, even though they don't look at all like it! Some people will call any weedy grass "crabgrass".

Sorry, I'm in Southern California and it believe it's a tall fescue. And trust me, it's crabgrass! And I can't spot treat it because there's just too much. It's the original lawn that was here when we bought the house, so I'm not exactly sure.
It sounds like I'd be better off just starting over. And assuming that I use sod, how deep would I have to replace the soil to make sure I got all of the crabgrass / seedlings out?

Just removing the top inch should get 99% of the seed, unless a previous generation of crabgrass was rototilled in earlier. Good sod should keep most of what's left too deep to sprout. If it is sprouting from "roots", then it isn't really crabgrass.
Please don't think that I am picking on you. I have a lot of customers who insist that they have crabgrass, but after the crabgrass remedies don't work, they bring in a sample, and it turns out to be common bermucagrass, nutsedge, Johnsongrass, or suchlike!

Don't worry, I don't feel picked on! I just wish I was more knowledgeable so i wouldn't have to keep asking these silly questions. I'll try and post a picture or two soon. If it's not crabgrass, are these other types (as you listed) easier to get rid of? Are they common in Southern California?

I've posted a few pictures of what looks like crabgrass. Can anyone confirm?

Also pictured are my Cordylines that have some type of damage. Any suggestions?

I looked at the pictures, and that is actually centipede grass (Eremochloa ophiuroides). It is treated the same way as crabgrass, even though it is a much tougher, perennial grass, that roots as it grows, unlike crabgrass. It isn't rhizomatous, but I would take up two inches, just to get the bottom of the thatch, and any stray stolons there. It may still sprout from seed, but regular fertilizing actually discourages centipede grasss, since it prefers poor soil to grow. One option, if you can stand the coarse texture, is to give up and let the centipede take ove as your lawn--particularly practical if you live near the beach.

I'll look over the cordyline question, but I may not be much help there. They don't normally survive the summer here!

Thanks Tug. So, centipede grass, huh? I'm not sure I've ever heard of that before. Letting it take over may be an option, but I'm not sure I can handle the "sponginess" of the grass. When I mow the lawn, I feel like I'm walking on a foam pad!

Ok, so I've been doing a little research on centipede and St. Augustine grass. People actually TRY and grow this stuff! Amazing. Here, I'm trying to get it OUT of my lawn, and people are trying to make it grow???