Okay so once you have your video file downloaded, go on photoshop, click file, then go to import > video frames to layers. Choose your video, and then a window should pop up that looks like this:
Select “Selected Range Only” (which basically makes it so that you can choose what part of the vid to make into a gif). Click “Limit to Every 2 Frames” if you want to make it so that when photoshop turns the video into layers, it skips every 2 frames (it’s mostly to keep the gif file smaller).
Then, drag the little cursor thingy (ugh I have no idea what it’s called) on the video to get to the part that you want to make into a gif. Hold shift, and drag it as far as you want the gif to go. When you’re done, click OK.
It takes a while to load, but once it’s done, you can start editing your gif. Oh, make sure to go to Windows > Animation. That will open up a window showing every frame in your gif:

It’s okay if the part of the video you selected isn’t exactly the part you want in your gif (it can go over by some), just make sure the part you want is in there somewhere. On the Animation window, you can select the frames you want to take out, and click the little trash can next to the Animation window’s scroll to delete it.
If the gif is going to fast or too slow for you liking, right click the little number under the picture of a frame:

and choose the speed you want. To change the speed of all the frames at once, highlight all of them (click the first frame, hold shift, and then click the last frame), and right click any of the frame’s speed number. :)
To change the size of the gif, go to the Layers window (if the window isn’t there, go to Windows > Layers), and highlight all the layers. Then, go to Image > Image Size, and type in the size you want (Photoshop automatically keeps it so that the proportion stays right).
Blah, I’m getting lazy, so if you need help editing the color or cropping out certain parts, just ask me!
Anyway, when you’re done editing, click File > Save for Webs & Devices. A window will pop up, and go to the tab labeled “Optimized.”

On the bottom of that window (the area in red), is the size of your gif. Tumblr has a size limit of 500k, so if you make any gif over that, it won’t work properly. Make sure to keep it under.
Other ways to lower the size of your gif, is by changing the ‘Colors’ section (the area of the pic in blue). Normally it will be 256, but if you change it down to 128, the size of your file will get a lot smaller. The ‘colors’ section indicates the number of colors that will be used in your gif. Obviously 256 will have the greatest range, and will make your gif look nicer in terms of color (but a lot of the times, when I end up using 128, I don’t see much of a difference compared to 256).
I also find that lowering the dither (area in green) will lower the size a great deal (just moving it from 100% to 99% makes a big difference!). I don’t know what dither really does, but it has something to do with the quality. Another way to do it is by lowering Lossy (area in orange). It also has something to do with quality, and changing it from 0 to 1 makes a big change in size.
If you want a preview of your gif with all these changes, click Preview (although I have to warn you, the preview will open on Internet Explorer). Also, if you’re not sure what changes to make on this window, you can go to the 4-Up tab (two tabs over from Optimized), and it will show 4 different versions of your gif, each with different changes.
Lastly, make sure the area in purple says GIF. Then click Save. And you’re done! :)