Most dealers charge around $150 to replace a worn serpentine belt. My local Toyota dealer quoted $95 for the belt alone. For around $25 and about 30 minutes worth of time you can change this belt very easily yourself. All you'll really need is a socket set with a 14mm socket (and perhaps some smaller sockets to remove some additional screws/tubes for access).
Probably the most important thing in this process is just to get the right part. The stock belt that I removed from a 2004 Tundra Double Cab V8 with AC was labeled "Dayco 6pk2300 - 90080 91172". Just make sure that you get the right belt for YOUR vehicle. Note some belts are with out without AC specific.
Here are 2 belts that are direct replacements for the stock belt:
Gates K060908 - I used this and it fit perfectly
In the spirit of a picture (or video in this case) is worth 1000 words, have a look at this great video which should be about the same process for 2000-2006 Tundras with the V8 engine.
I was actually able to remove the old belt and install the new one without removing the airbox or any of the radiator hoses. I do have pretty skinny arms and I did get a little scraped up, but I was able to get it done. You should be able to discern for yourself how much room you'll need to clear by looking at it.
Find the accessory belt routing diagram on the the frame under the hood if there is one, see below. This will help you identify the tensioner pulley and remember how to route the new belt. If you DO NOT have a routing diagram on the frame, take some pictures of the old belt routing before removing it to reference later just in case you forget or don't want to memorize it!
Use the 14mm socket and bar to turn the tensioner pulley to the left and relieve some of the tension on the pulley and remove the old belt.
Route the new belt over the pulley system according to the routing diagram leaving the tensioner pulley for last. Use your fingers to feel and make sure the belt seats in each of the pulleys. Pull the socket on the tensioner down to the left again and slide the belt over the tensioner to finish.
Finally, Inspect Serpentine Belt Tension
Following along with the diagram here, inspect the tension marks that you should see on the back metal housing of the tensioner pulley:
Once you're sure the belt is routed properly and seated in each of the pulleys correctly, start the engine and check that the belt is turning without issue. Congratulations, you're done!