How I make gifs.
I use VLC player and Photoshop CS5 to make my gifs. Older versions should work though. You can download a 30 day trial of Photoshop here and you can download VLC for free here.
First, make sure the episode/movie you’re making the gif from is high quality. Obviously if your video is low quality the gif will be too. Open it up in VLC player and find the part you want. I usually watch the episode and make gifs as I’m watching. (Unless I have a specific scene in mind.)
If you’re making a gif of a subtitled anime, you might want to turn the subtitles off, unless the subs add humour to the gif. If you want them gone go to Video > Subtitles Track > Disable. If you don’t see the disable option it means the episode is hard subbed and you can’t turn them off.

Sometimes it helps to slow the video down, especially if the part you’re wanting to make a gif of goes by really quick. Go to Playback > Slower.

Once you get to the part where you want your gif to start, pause the video and go to Video > Snapshot.

Once you do this a snapshot of the screen will automatically be saved in your Pictures folder.

Keep playing, pausing, and making snapshots until you have the entire scene you want. Try not to make it too long or else it will be too big to upload on tumblr. I usually have 6-12 frames.
Open Photoshop. Go to File > Scripts > Load Files into Stack. Select all the snapshots and open them. Make sure to give them time to load before you start the next step. You will see the snapshots load on your layers panel.

Make sure the Animation window is open.

On the far right of the Animation window is an arrow, click it to open up a window. Go to ‘Make Frames from Layers.’ In the same menu, go to to ‘Reverse Frames.’

On the Animation window, play the gif. Adjust the time between each frame until you’re happy with the way it looks.

I always edit my gifs with the tools found in the Adjustment panel. I mainly use Curves, Brightness/Contrast, Exposure, and Vibrance. I occasionally use Photo Filter too.

Next, you need to resize your gif so it can be uploaded to tumblr. Tumblr requires gifs to be under 500 x 500 and 500kb 1mb total. I start by resizing the height of my gif to 500 and go from there. Go to Image > Image Size to do this.

If you want to you can add a watermark to your gif. I don’t always remember to do this but when I do I make sure it’s subtle. I make the font small but still easy to read and I turn down the opacity so it isn’t too distracting. The text layer should be above all the frame layers. When you’re adding text or editing make sure the first layer is always selected.

You also should make a blank layer, use the fill bucket to paint it black, and drag it all the way down to the bottom. Sometimes when you save a gif it gets this dashed white border around it and the black layer at the bottom helps prevent this. Make sure the layer is below all the others.
To save your gif, go to File > Save for Web and Devices. Check that all the settings match the settings circled in the screenshot below. Also make sure the size of your gif is below 500kb 1mb.

If its not under 500kb 1mb see if there are some extra frames you can delete. If not, you will have to resize it. If it’s not under 500kb 1mb it won’t move on tumblr. For some reason when I play my gifs on this save for web and devices window they always appear slower. So make sure you preview them outside of this window. You can also reduce the amount of colors in the gif. Just keep in mind if you reduce it to much the gif won’t look as good. I find reducing it to 250-200 makes a big difference. Especially if you don’t want to resize your gif.
If it looks good, save it (make sure you save for web and devices) and you’re done!
Here’s my finished gif:

I hope this helped and if you have any questions message me!