I am new to Linux. I loaded Ubuntu 16.04 32 bit OS on to a Compaq CQ-58. On public wi-fi it loads pages at a blistering speed. I was astonished how fast Facebook loaded. What I wanted to know is it possible to get internet using a 4G USB dongle?

Do you mean a wireless dongle?

Yes. However, you need to research any dongle you consider very carefully. Linux support from manufacturers of wireless dongles is rather spotty. Verify that it works with Linux before you buy.

Yes it is a wireless dongle that gets signal from the 4G network. It is a Huewei E353T , revision CP1353UM if that is any help.

Stick it in - what happens ?.

A web search for "Huawei E353T linux" turns up a number of articles.

I have no personal experience with that make/model.

Yes.

What sort of device - the type you tether to the machine directly (by plugging it in), or the type that provides a WiFi hotspot that you connect to (plugging in is only for charging)?

In both cases the answer is yes.

If you've an android phone you could always use your phone as a WiFi hotspot and avoid having to have another data contract for your dongle.

Has the dongle been set up using Windows? I think that will have already set up the device, and the trick is now to persuade Linux to use it. Its driver has been available for Ubuntu for some years, so there should be no problem there. This site seems to offer a useful guide
https://www.maketecheasier.com/setup-usb-modem-linux/

One piece of advice. When you use a router, it has a firewall between the internet and your local network (i.e. the router and the computer). When you use a dongle, you become part of the internet, so get a firewall enables on your computer! This will do it from the command-line terminal:

There is a way to discover all the hardware that a particular kernel has but in this case I'd think that many of the dongles will work. I've used more than a few. Some however are not fully 4G LTE. Many of the usb tethered will drop to 3G speeds and your ISP may have some limits.
I used to use a few of the usbs but now use a LTE Netgear LB1120.

Just a note, I doubt it will be blistering fast, after all, 4G is just a sales phrase and has no real guaranty of service.