You can start them by running an infected file - "infected" means that some other instance of the malware has added a copy of its code to a previously safe executable program, so that when you run that program, it also runs the malware code.
When a PC boots, one of the first things it does is load the first block of data on the hard disk: normally that contains the Master Boot Record, which is a tiny program that finds a bootable operating system (Windows, Linux, whatever) and loads it.
But it's possible for that program to be modified, so that it loads some malicious software every time you boot your PC.
A more common possibility these days is software hidden in USB flash drives: Windows traditionally looks for a file on every removable device (floppy, CD, USB drive) called Autorun.inf, which tells it which program(s) to run automatically; so it's quite easy for a program to lurk there and be loaded when you plug in your USB device.
10-15 years ago, this autorun feature was supposed to be a convenience, but nowadays it's downright dangerous.