I actually have different ways of making my gifs. Lately I’ve been combining the Photoshop filters “Smart Sharpen” with “Reduce Noise”.

There’s also a Photoshop plugin that smoothens and enhances your images, called Topaz (the ones I used are called Detail and DeNoise). Topaz can make big differences to the image, and overdoing it will make it look waxy. Play around with the settings, and keep in mind - less is more!

Lastly, some gifs are only sharpened.
Which method I use depends on the quality of the clip I make the gifs from :)