I'm only concerned here with free software. There's plenty of suitable examples available which compare favourably with expensive commercial software. This is how it's done in Paint.NET.
First go here & download Paint.NET v3.5.4 (or latest version) http://www.dotpdn.com/downloads/pdn.html
Installation is quick & simple. Extract the zipfile & run Paint.NET.3.5.4.Install.exe. I chose the Quick install option.
Before we begin I would like to emphasize that you will get the best results from working with the original screenshots saved in an uncompressed format. Every time you open & save an image in a compressed format like JPEG the quality suffers.
OK, now we're ready to make a start. Let's suppose you've taken a masterpiece & wish to post it on the forum. Like most things on the computer this takes much longer to describe than actually do. Run Paint.NET from the desktop Shortcut & open the saved shot - (File > Open). My example was taken in FSX with the onboard screengrab feature (V key). It was saved in BMP format at the native resolution of my monitor which is 1440 x 900 pixels. It will need resizing to meet the forum limit of 1024 pixel width.
Click Image > Resize on the Paint.NET menu bar. This option window will open.

Leave the Resampling option on the default 'Best Quality' setting. Make sure the 'By absolute size' radio button