The only way to know is to read the details of the application either before downloading it or on the vzw.com website. Usuing the MobileWeb app will certainly bill you MBs but the usage you can get out of it is pretty generous. Typically you can get about 30-50 different pages in the mobile web before it equals 1 MB @ $1.99. Or if you have a phone with a HTML browser (Voyager, Glyde, Versa, EnvTouch) then it's a little smaller at about 15-25 different pages =1 Megabyte.

Keep in mind the usage isn't always up to date, data usage especially can take several weeks sometimes to be reported on the website. So check back often.