To create a USB installation device, you will need:
an 8 GB USB flash device/drive/stick. If the iso file is smaller than 4 GB, it is possible to use a 4 GB USB device, at least with some of the methods. Files on this USB device will be erased, so backup the files you want to keep before making the device bootable. Some of the tools require that this USB device is properly formatted and mounted while other tools will overwrite whatever is on the target device. Please follow the instructions for each tool.
Check with md5sum (or another checksum tool) that the download was good.
Notes about speed
The most common USB ports and USB flash drives work according to the USB 2 standard. Booting from USB 2 from a live drive is faster than from a corresponding CD/DVD disk. Standard USB 2 flash drives have rather slow flash hardware, with read and write speed much slower than the transfer speed of USB 2, so it is worth checking if the speed is specified.
USB 1.1 is also possible to use, but it is very slow, slower than a corresponding CD/DVD disk.
Hardware according to the USB 3 standard is much faster than USB 2. So if you have a USB 3 port and a USB 3 flash drive, booting and running will be as fast as from an internal drive (SATA or IDE) or an external eSATA drive (usually limited by the speed of the memory access). A USB 3 SSD flash drive has very fast flash hardware, and there are USB 3 pendrives with specified high read/write performance. The market changes quickly, so it is worth checking on the internet, which brand and model to select to get the best buy 'today'. Please avoid USB 3 pendrives with slow memory cells.
An SSD with SATA interface and an external box/enclosure or adapter do not cost more (2020) than some higher quality pendrives of similar size, and such an SSD performs much better. The only disadvantage is that it is more bulky so it is more convenient to use a pendrive.
USB 3 flash drives (sticks, pendrives) can be much faster than USB 2 flash drives also in USB 2 ports, because the flash hardware is not limiting the transfer speed. For the same reason a USB connected HDD is also much faster than a USB 2 flash drive.
USB 2 flash drives are particularly slow when there are many small files to read and write. This makes them very slow when running persistent live systems and 'installed systems' (installed in the normal way, but to a USB drive). Also the lifetime (number of write operations on a memory cell) is much higher with the high quality hardware in USB 3 flash drives. But still, you should use noatime in fstab and use swap only for extreme situations to avoid excessive wear.
A LED (light emitting diode) helps you avoid unplugging the USB flash drive too early (while it is saving data from the buffers in RAM), and decreases the risk of corrupting the file system.
See also the following links
Standard USB 2 flash drives are good for normal live systems. Typically the speed is between 4 and 20 MB/s.
USB 2 flash drives work, but USB 3 drives with specified high read/write performance (or even USB 2 HDDs) are recommended for persistent live systems and 'installed systems'. In the beginning of 2020, it seems that there are no really fast pendrives below 32 GB.
Notes about size
Edit 2023-09-29: Heads up
Please notice that Ubuntu Desktop and its community flavours (Kubuntu, Lubuntu ... Xubuntu) grow. Each new version comes with a bigger iso file. Lately they grow faster than ever, mainly because some tools are distributed as snaps.
This means that you need bigger USB drives. Ubuntu Desktop 23.04 and newer versions will need an 8GB USB drive (the iso file exceeds 4GB).
Some community flavours, particularly the light-weight Lubuntu and Xubuntu continue to be small enough to fit when cloned to 4 GB pendrives.
Ubuntu Server grows too, but slowly compared to the desktop versions/flavours and is also small enough to fit when cloned to 4 GB pendrives.
Unless you already have a 4 GB drive, you are recommended to get one with at least 8 GB, hence the general recommendation above.
4 GB is enough for 'CD size' iso files as well as many but not all 'DVD size' iso files. A live (live-only) pendrive can be cheap, small and slow with at least 4 GiB for Ubuntu Server, Lubuntu, Xubuntu and 8 GiB for standard Ubuntu Desktop and the other flavours of version 22.04.x LTS. If you are not sure, please check the size of the iso file and get a pendrive, that is big enough for it (with some margin because the real size may be smaller than the nominal size (the advertized size).
If you want a persistent live system with a decent size casper-rw storage, you need at least 16 GB (8 GB is possible, but might soon run out of space).
If you want an installed system you need at least 32 GB (16 GB is possible with Lubuntu, but might soon run out of space).
In 2023, it seems that there are no really fast pendrives below 32 GB. If you want a fast system, install it into a pendrive that performs well in a test, even if it is 'bigger than necessary'.
Notes about bootability
Most but not all USB pendrives are reliable for booting, even many of the slower ones, and they are much cheaper, and should be OK particularly for regular read-only live drives (without persistence).
Some computer hardware and some operating systems have issues with certain ports. And some USB pendrives just have issues also. Some of them cannot be used for booting. They are made to be mass storage devices, and have not exactly the same electronics and firmware. Some USB pendrives and computers 'do not like each other'. The pendrive might boot another computer, and the computer might boot from another pendrive (everything else being the same).
This is a link to test by Pendrivelinux including bootablility of USB flash drives. This test was made a few years ago. The cheap and slow Sandisk Cruzer Blade can be added to the list of reliable pendrives for booting. I have used it extensively for years and it has failed only once (chainloading from Plop in a very old computer). This link shows a bootability test in January 2014.
The flash hardware
This link to a post by DuckHook in the Ubuntu Forums describes how a flash drive works, and how it can fail, first getting read-only, then totally 'bricked'.
Can't format my usb drive. I have already tried with mkdosfs and gparted - Analysis of the problem - This link can help you find out if there is a hardware problem or 'only' a software problem (damaged partition table or file system).
The following link describes various hardware problems and what can be done to repair a USB stick/pendrive/flash drive
http://www.wikihow.com/Repair-a-USB-Flash-Drive. Look for the tips and warnings!