Time Machine - How to Back up a Mac
You will need an external hard drive that your Mac can access. This is easiest with a USB drive that can be found at many stores/websites. The simplest way is to simply plug the external drive into your computers USB port and then follow the instructions at the web link below. Alternatively the external drive may be installed on a USB port present on most wireless routers. Some setup may be required to allow access but once done you can use the hard drive to back up any/all Macs you have in your house wirelessly.
The external hard drive needs to be big enough to support this. As a rule of thumb, it should be at least twice as big as the drive(s) you are trying to back up. If your Mac has 500k on board storage you should get at least 1TB. If your Mac has 1TB of internal storage you should get at least 2TB. If you have more than one Mac to back up you will need add them up to determine how big it should be. Bigger is better if you can afford it because that will allow for a longer history from which you can recover lost files. Time machine does a full back up the first time (this can take a long time) and then does incremental backups, only backing up things that have changed. When the back up drive is full, it will delete the oldest back ups to make more room.