This can certainly be done, and is the most usual home network setup.
To try to give step by step instructions would be a waste of time here. Too many variables and discrepencies would occur. If you are running Windows XP OS on your laptop, just go to "My network places" and click the link to "Set up a wireless network for a home or ....". I'm not familiar with the Vista OS, but I would guess the links are similar. Windows will guide you through the setup.
Or, if the laptop is just purchased, read the documentation that came with it. It will either be electronic (a file on the hard drive) or hard copy. Your Verizon installer should have given you a "Internet Quick Ref" sheet containing the SSID and WEP Key of your router. You will need these for the wireless setup.
If you have a Mac, I congratulate you, but can offer no assistance.
Are you talking about too many characters when logging into the Actiontec router? If so, that is just a security feature of the router to prevent someone looking over your shoulder from seeing how many characters you are entering, and to confuse them on what the password really is. Just ignore it. Type what the password really is and you should get in just fine.
Now, why are you logging into the router at all? Should not be necessary to get the laptop working wirelessly. The initial password for the Actiontec is "password", but that must be changed at initial login - many techs change the password to "password1" when they do the install.
Once you get this laptop working correctly, I suggest you do a little research on wireless security and figure out what if anything you want to change. The default encryption used in this router (WEP) is really pretty weak, you should consider changing to WPA. You should also change the login name and password on the router to something only you know. There are other security steps you can take, such as MAC address filtering and SSID broadcast, but most experts seem to think they are pretty worthless. I don't, I view it as anything that makes the intruder work a little harder may just discourage them. There are plenty of easier targets out there.
Anyway, to access the internet with the laptop you should not need to log into the router.