What would be the proper way to make a backup of the computer? Is there a way to backup so if I formatted or replaced the harddrive I could just duplicate the drive? Or make an exact duplicate of the drive I have now so I don't have to reinstall all the programs?
Making an exact duplicate of the harddive is different than making a backup of the data on the harddrive, because the exact duplicate also includes the operating system and all of the applications/programs.
For general purpose backing-up of data, a backup tool (like Windows Backup or an equivalent) will copy and compress the data into another file somewhere on a different drive which you later can access and uncompress/expand to retrieve your data.
To make an exact duplicate of a hard drive, you will need what is known as imaging software (do not confuse the term "imaging" with images related to graphics). I am not endorsing any particular imaging software, but two consumer grade products include Norton Ghost, and Acronis True Home Image. I have used both. Each has its own way of doing the job. But, when done, the image of the hard drive is saved as a very large file on another drive you choose. If the source drive fails and needs replacement with a new unformatted drive, you can use the imaging software to put the image onto the new drive, and it will be exactly like it was when the image was created.
You can also use this technique to upgrade to a larger drive if yours is getting full. Make an image. Get a larger drive. Put the image on the larger drive using the option that lets you put it on a larger drive (instead of a same-size drive).
Imaging takes a lot of time because it backs up the entire disk, BUT, it saves a lot of time when you consider how long it takes to manually install an operating system, do its updates, install an office suite, do its updates, install any other stuff you want, like printer drivers, specialized drivers, etc. and their updates and then later to restore data.
Each type of backup has its strengths and weaknesses. Some people use a combination of them. Image once or twice a year, and do regular backups more often.
Hope this helps,