In my experience most usb modems have native support in Mint. Follow these directions and hopefully you'll be up and running.
Log into mint and plug in the modem. Wait for a few minutes till the light changes to green (if it has that feature, if not just wait for a few minutes).
Right click on the network manager icon --> edit connections --> mobile broadband --> add. the network manager icon is the one next to the date and time on your taskbar.
In the popup that comes up, your device should be listed at the bottom in the dropdown. If it's not there, just wait for a few more minutes and try again. It sometimes takes as much as 5 min before the device is recognized.
After that just click next, following the directions for country and service provider. Click finish.
In the new popup, you can give your connection a name at the top. Leave everything else as is. close.
Right click on the network manager icon --> Enable mobile broadband.
Left click on the network manager icon --> click on your connection (The name that you assigned it will be displayed)
You should get connected in a few seconds.
Please post back if you run into any issues.