Well, which Ubuntu do you want?
The Ubuntu desktop installer with the Unity desktop environment is freely downloadable as an ISO file, but you may wish to look at other versions of *buntu, especially since your destination machine, that old IBM-vintage ThinkPad, may be a little slow with Unity. Other official distributions you may consider are listed at Wikipedia, and include:
All of those use less memory and respond faster than the Unity desktop environment in the official Ubuntu distribution. This is especially useful if your old Thinkpad's RAM is less than 2GB.
Once you have decided which you want to use, download its ISO file. Download the 32-bit version, since your IBM ThinkPad is old and may not have the RAM recommended for 64-bit versions of *buntu. (We can talk about changing to 64-bit later, once we have it up and running in 32-bit).
When you have its 32-bit ISO file completely downloaded, then we follow the official Ubuntu instructions at http://www.ubuntu.com/download/desktop/create-a-usb-stick-on-windows
Step Zero is to download and install a small, and harmless, app on the Windows PC. The app, the Universal USB Installer, allows you to turn a USB flashdrive into a LiveUSB. (I recommend using at least a 2GB flashdrive, although some of the versions above will let you use a smaller flashdrive. A larger flashdrive is AOK.)
Once the Universal USB Installer is downloaded and installed in Windows, Step One is to launch that app, and choose the version of *buntu you downloaded.
Step Two: Click on Browse to find the ISO file you downloaded for it, and Open it.
Step Three: Choose the drive letter for your USB Flashdrive, and click on Create.
Step Four: Once created, close this app, and then in the Windows Desktop, in the Tray at lower right down by the clock, click on the USB icon and safely remove the flashdrive.
Step Five: Plug the Flashdrive into the IBM, and power up. Press {F12} to call up the list of bootable devices, and choose the USB Flashdrive.
If the Flashdrive does not appear, then power off, power back up, and press {F1} to go into the ThinkPad BIOS, and there configure the ThinkPad so the USB FlashDrive is a bootable device, then save the change, reboot, and press {F12} to pick the flashdrive for booting. https://help.ubuntu.com/community/Installation/FromUSBStickQuick#Start_the_Ubuntu_installer provides extra detail on this.
Step Six: You now have booted from the LiveUSB, which will give you the choice of running *buntu from that Live USB drive, or installing *buntu on your hard drive. Running from the LiveUSB is AOK; it lets you 'try before you buy', and experiment to see which version of *buntu you like the best.
Step Seven: Once you know which you like, then click on the installer, which will ask you several commonsense questions, and then reboot the PC. When the screen goes blank in the reboot process, remove the USB Flashdrive, and your ThinkPad will boot into your brand new *buntu from your hard drive.