In UEFI or BIOS, most systems have a “boot order” menu, where the user can tell the system which storage device to scan first for a boot loader. It is usually necessary to explicitly change the boot order to make the system look to the removable media first. (Most systems attempt to boot from fixed media first to avoid the possibility of a malware infection. Some systems even reset the boot order so that the next manual reboot returns to checking the fixed media first.)
It is usually best to plug in your USB stick before you power up your system. Then, when you enter your BIOS or UEFI menu, detected bootable devices should be displayed in the “boot order” menu. Set your USB stick as first, save your changes, and exit the menu. This is how my systems have worked, at any rate; YMMV.