Because I have seen quite a few posts about using 3G dongles and accessing the Internet when no WiFi is available I thought I'd put something together in one place, that may help. I am excluding tethering to phones here because that is pretty much another whole thread.
First, the issues with a 3G dongle. (modem)
Android, as yet, has very little support for plugging a 3G dongle into a USB port, (assuming you have a USB port) due to a lack of drivers. Those drivers are frequently specific to the carrier the dongle was obtained from. But there are a few that do work with many Android tablets. Here is a list of a few that work and how to enable them.
How to setup your 3G modem
How to setup your 3G modem
Note, for that to work it specifically addresses Android v 4.0
If you don't have access to those specific 3G modems or you don't have a USB port you can use a portable router that supports a wide range of 3G modems. Here is a list of broadband (mostly 3G) modems supported by Zoom Telephonics' portable router(s).
Zoom Telephonics - Mobile Broadband Modem and Smartphone Compatibility Information
No 3G modem?
So, let's say you don't want to invest in a 3G modem due to the contract cost. There are several portable routers that will allow your WiFi enabled tablet to connect to a wired network. One of those is a TP-LINK TL-WR702N N Nano Router. Another is an ASUS WL-330N3G Mobile Wireless Router. Both of these can also act as a WiFi extender or a WiFi bridge, but can be configured as a WiFi to wired network device, (using a computer for the initial configuration). The ASUS device also has limited support for some 3G modems. This is a short list as there are many portable routers that will do the same. The TP-LINK is particularly inexpensive.
ASUS also makes a USB to Ethernet adapter that works with Android 4.x. http://www.asus.com/Peripherals_Acce...able/#overview
Another option is what is commonly called a MiFi device. This is a cellular modem, (about the size of a deck of cards or smaller), typically purchased from a cell phone provider that communicates with your tablet via WiFi. (no ports required). The drawback is that it also typically carries a fairly steep monthly contact cost. However there are some benefits. You can typically connect as many as 5 devices at a time. Since you could use it for your tablet, (1 or more) and a laptop and even your phone, and it works even when you have lost your Internet connection due to mechanical failure in the provider's system, it makes a great emergency backup. This would also work on any WiFi equipped desktop assuming you have a good cellular signal.
Because the MiFi devices is so flexible it's like having a cellular connection with only one contract for multiple devices. I won a Verizon model MiFi and it enabled me to use minimum required data plans for my smart phones, so it is saving me some moey there that offsets the cost of the MiFi plan.
Anyone with other suggestions is welcome to chime in.