First off, you'll need to have a fresh install of terraria. To do this simply go to your steam library within the steam application and right click on Terraria and then click on "Properties" > "Local files" > "Verify integrity of game files..."

Then wait for it to validate the files and then a download will start, which is essentially steam re downloading the original game files therefore leaving you with a fresh install of Terraria.

Now you'll need to find your Steam game library path within the File Explorer application. If you don't know where this is, the default path is "C:\Program Files (x86)\Steam\steamapps\common" unless you have changed it yourself, in which case you'll know what you're doing here.

Now that you are here you'll want to create a copy/backup of your original Terraria install by simply right clicking on the file named "Terraria" and clicking copy and then right clicking again wherever you would like to keep your backup and paste it there. Then wait for it to copy, which depending on the speed of your desktop/laptop will not take long at all. If you want to keep the original version of the game you can change the name of it before you replace the files so the original .EXE doesn't get replaced.

Now you'll need to go to the tModloader web page: https://forums.terraria.org/index.php?threads/1-3-tmodloader-a-modding-api.23726/
then scroll down until you see the blue text that reads "Windows" in blue next to "Steam" which is regular white text. Click this.
Then it will automatically start to download the files required to play modded Terraria. To open this file you will need either 7zip or WinRar which you can get here:

http://7zip: https://www.7-zip.org/download.html

http://WinRar: https://www.rarlab.com/download.htm

Then go to the location of which you downloaded this file and extract the containing files into your Terraria directory which you should still have open from before. Again depending on the speed of your desktop/laptop this will not take too long. When it prompts you to "Replace the file(s) in this destination" you will want to replace them all, as these are all required to run the modded version of Terraria.

To install mod, once you're in the main menu you will want to click on "Mod Browser" and just browse the different mods available. There are plenty of great mods to try out!

Now that you have downloaded the mod(s) you wish to use, you'll need to activate them, to do this simply go to the main menu again and click into the "Mods" option and at the bottom you should see an option to "Enable All" click this, unless you have mods in the list you dont want to install at this time, if so just click "Enable" on the ones you would like to use and then click "Reload Mods" and it should bring up a progress bar which means it is loading in the mods you have enabled.

Congratulations! You can now play with the mods you installed, have fun!!