Downloading videos, editing them in Camtasia (or which every you use) and converting to .gif
This tends to be the best site for it, as you can even change everything from the audio quality (not needed for .gifs but in case you wanted to make videos) to resolution.
You can then use it to upload your video and turn it into a .gif.
It's online, so no need for software to install. You can even use it to download audio off of Youtube for those hard to find songs.
I used it to make this video years ago when Eli won his first SB http://youtu.be/r9ngQnf5An8
LOL off topic, but look at the comments from irate Patriots fans.
I'm going to be making a few Internet Meme .gifs this weekend BTW and will either re-post them in this thread or make a new thread. I'm the one who made the Victor Cruz meme which can be found here : http://memegenerator.net/Victor-Cruz-Salsa-Dance