Usually doing a macOS upgrade is pretty much straightforward. With that said: it doesn’t hurt to be prepared.
The first thing you should do before you upgrade your Mac is, you guessed it. Backup your data!
With Macs this is done using Time Machine. The easiest way is to get a external hard drive. Plug it in your Mac and answer yes to the question if Time Machine can use this drive as a backup drive. Then let it sit for a while. Depending on how much data you have it can take several hours. Let it sit overnight if you have to.
If your Mac is very old you may not have Time Machine. If this is the case you will have to do some more manual work meaning you have to copy your data over to the backup drive yourself. If you store your documents in your user folders different folders. Such as documents, music, pictures etc. It should be enough to copy these folders to an external drive. Remember to get the Desktop and Downloads folder as well.
You could also use SuperDuper! to clone your Macs internal hard drive to the external one. Then afterwards you can pick and choose files you want to have when you got the new system up and running. This is an approach I like. This enables you to do a clean install of the system and some times its best to just wipe everything and start fresh. It is very time consuming though.
Do I HAVE to reinstall fresh?
No. I understand that time is money and for some of you it is essential to get up and running ASAP. Over the years Apple have refined and made the upgrade path more smooth, streamlined and secure. That doesn’t mean it is always this way, but there are some things you can do to minimize the risk of upgrade griefs.
A quick and easy solution: Prepare your Mac for Mac OS Sierra. This is software that scans your Mac and safely get rid of literally all junk you have gathered during the years. It will free up space on your drive, clean up your mac and get it ready for upgrade. I have reviwed the software myself in this article: 9 Ways To Free Up Space And Clean Macs. I have a tight control of my machine, but I was surprised how much the software actually found. The software is made by MacPaw Inc. They are nice guys and not like some of the others out there.
If you are wondering, macOS sierra is installable on Macs as early as 2009. Check the “prepare” link above for more info about that and minimum required specs.
Will my applications work?
If the application you use is actively maintained chances are that it will work. Maybe it just needs an update. Not all developers are quick with updates so if you use something that is mission critical you should do a Google search of the application name to find the developers website. Then check if it mentions anything about a new OS release.
When this is done it is just a matter of opening App Store and clicking that upgrade button.