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I’m pretty sure there are easier ways to make gifs but this is the way I make them. The good thing about this is that the only program you’ll need is Photoshop, nothing else.
Hope this helps!
STEP 1
Open Photoshop and go to File > Import > Video Frames to Layers…

STEP 2
A new window will open up for you to select the video you want to gif from. Once you find it, click Load.

TIP: If you can’t see the video, go to File name: and type ”*”. Hit enter and you’ll see all your files.
STEP 3
Another window will open up that looks like this:

Four things to note:
1. Make sure this is selected. You don’t want to gif the whole video and loading all the frames will take forever.
2. I usually select this when I make gifs for Tumblr. It helps make the file smaller.
3. Make sure this is selected too.
4. When selecting the scene you want to gif, move the slider to the beginning of the scene and hold shift while using the arrows (encircled) to move to the end of the scene.
Once you’re done, click OK.
STEP 4
Now, the project window should be open.

Make sure that the Layers (1) and the Animation (2) windows are open. If they aren’t, go to Window then select Animation and Layers.
STEP 5
Gifs for Tumblr can’t have too many frames. Most usually have a maximum of 20. Or there may be a part in your selected scene that you want to get rid of. Either way, you’ll have to delete some frames.

Select the frame you want to delete and click the Trash button at the bottom. Do the same for its corresponding layer. Repeat as necessary.
STEP 6
If you click the play button on the Animation window, you’ll see how the gif will look. Most of the time it’ll play too fast. You’ll have to change the frame delay.

Select all your frames by holding Shift and clicking the last frame. Then click the little black arrow at the bottom of any frame and choose the delay you want to use. Click Other… to type in a delay that’s not on the list.
TIP: It takes a bit of trial and error but I usually go with 0.1 seconds.
STEP 7
Once you’re happy with how the gif plays out, it’s time to make adjustments to make it Tumblr-friendly. First, the size. Go to Image > Image Size… and this window will open up:

Type in 500 pixels for the width since that’s Tumblr’s maximum width for images. Of course, you can make it any width you want. Click OK.
STEP 8
You may want to do other adjustments to make the gif pretty. Just make sure that when you make adjustments, all the frames in the Animation window are selected and that the adjustments are applied to all the layers.
TIP: It’s easier to make adjustments using Adjustment Layers (Layer > New Adjustment Layer) rather than doing it over and over for every layer. Just be sure that your Adjustment Layers are on top of all the other layers:

STEP 9
Almost there! Go to File > Save for Web & Devices…

STEP 10
A new window will open up that looks like this:

Make sure that you’re on the Optimized tab.
This is the tricky part. Tumblr will only accept gifs below 500 kb. To check, look at the bottom left corner of the window:

Your task now is to change some things to get the gif as close to 500 kb as possible.
On the right, you’ll see a bunch of settings.

Seven things to note:
1. This is where you choose the file type. Select GIF. Of course.
2. These are color options. Click them to see what they do but I usually stick with Selective.
3. These are dither options. Again, just click them to see the effect. Dither is necessary to make the file size smaller. I usually choose Pattern.
4. If you choose the Diffusion dither option, you can change the percentage of the dither. Smaller percentage means more noise or dotty things on your gif.
5. This is the number of colors your gif has. Less colors means smaller file size.
6. Make sure this says Forever so your gif is an endless loop.
7. Use these to preview your gif.
TIP: Keep playing around with the settings and the number of frames your gif has and the adjustments you make to it. It takes a lot of trial and error to get it to look the way you want it to.
RESULT

Good luck!