What you will need for this to happen:
-A USB stick (The size will depend on how big your derivative of linux will be, but normally a 2gB will get you home safe)
-UNetBootin (The Torrent at the top of my post)
-Optional-An image (Iso) of the linux derivative you want to install.
So I got a screenshot to make explaining what every section of UNetBootin does easier to understand.

So there are three options on how to install and one option on choosing a destination.
I'll go through them one by one.
Note The difficulty increases as we go down the options.
[Beginner]Distribution: These are the supported linux derivatives. Simply choose one and select your USB destination then click ok.
What this does is it will lookup the version of linux you want in the repository ( A "download stronghold" of nearly all linux versions ever made) and once its found it, it will download it and then install it to your chosen destination. I will agree this is a very easy method but will require quite the time.
Time Required: (Varies with internet speeds) But presuming you have 100kB download speeds it would take about 119 minutes (i tried using a calc
All in all this is the option you select when you dont care bout letting it work in the background or you cant be bothered to get the images manually.
[Intermediate]DiskImage: If you have gone and gotten a DiskImage (ISO or Floppy, Although most of the latest will be ISO) then this is where you want to be. Simply select the image by clicking the three dots at the end of the input area and a window should popup asking you to direct it to the ISO.
Once thats done select the USB destination and hit ok.
What this will do is pretty simple, it will check the ISO you specified and make sure it has all the stuff required. Once thats done, it will initiate the extraction and copying process whereafter it will install to the USB you choose. All you needed to do was specify the correct DiskImage.
Time Required: Im going to presume you already have an ISO. So here it depends on which linux derivative you are trying to use.
I for one waited half an hour for ubuntu 10.04 and 1hour 15min for ubuntu 9.04. So if your trying to install a different derivative it might take even more or even less time.
[Advanced]Custom: Unless you know exactly what you are doing please leave these untouched!!!
If you're using this it means you know EXACTLY what you are doing so i wont need to explain kernels (etc).
So lets say you are cooking up your own custom linux this is where you want to be, choose you kernel, Initrd and options.
Choose your USB destination and click ok.
Now i presume this will only be used by either developers or people who are experiencing problems with the newer or older kernels.
Either way even if you mess about, it shouldn't do much harm given you're trying to put it on a USB stick.
Time Required: No clue. It depends on everything you set, so maybe an hour, maybe two or you could wait for five.
Destination "Other Drive"
This option does give you the choice to specify HDD's as the destination.
I left out the "show all drives" option in all my posts on purpose.
This shouldn't be meddled with lightly. Please triple check your destination when using this option, because you could mess up your current O.S if you choose the wrong HDD.
And thats it, Hope it work(s/ed) for you.