There are plenty methods of making gifs.
Here I’ll show you the easiest for me.

You will need two programs: Adobe Photoshop CS5 and KM Player. You can use previous versions of Photoshop, but some of them need Image Ready to make animation. So I suggest you to get CS5, just to save time. I can’t give you links for it, because I don’t want to be responsible for the source. You can google it though, there are plenty torrents and sites with a wide choice of downloads + keys.
Now back to the tutorial
1. Open video in KM Player, pause on a moment you want to turn into gif
Right click on the player -> Capture -> Frame: Extract
(if you don’t have a capture option in the menu, click Options -> Advanced menu)

You can leave the extract location as it is, but I create a separate folder on the desktop for the captures. Makes it easier to find them. Copy these settings, click Start and then Play on KMP. Pause when you think you got the whole scene you wanted.

Open your folder with captures and delete every second file. It makes the gif weigh less.
2. Open Photoshop. File -> Scripts -> Load Files into Stack

Use: Folder, click Browse and select your folder

Wait for the captures to load as layers. Open animation window(Window -> Animation). Click this button -> Make Frames from Layers

Click this button again -> Reverse Frames
3. Go to Image -> Image size and resize it whatever you like. The smaller the gif, the less it weighs. I like making big ones, so I resize it to 500px width
Now we are going to make the gif sharper. Click Dublicate Selected Frames in animation window

Make all the layers visible

Select Filter -> Sharpen -> Sharpen
We edited the first layer. Now select the second one and click Ctrl + F. Apply this to every layer.
Back to the first layer. Select Filter -> Noise -> Reduce Noise with these settings:

Apply this to every layer. Once you are finished, delete the last frame from animation.

Now the coloring. Select the top layer, click Create new fill or adjustment layer, choose Curves(I always use this adjustment because it’s my favorite, but you can also use Brightness/Contrast or Levels. They are a bit similar)

Play around with it until you get the brightness you like

I think my gif is moving too fast. So I select all frames and set 0.1 seconds time delay

The background here is still. I think it’s a good opportunity to make the gif weigh less. Select the first layer, press Ctrl + J and erase(using eraser tool) the part where your gif should move

To save your gif go to File -> Save for Web & Devices

As you can see, this gif doesn’t fit into the limit of tumblr. It should weigh less than 500k. Plus there’s noise all over it. Here are some options to fix this:
1) Make layers Black&White: Create new fill or adjustment layer -> Gradient Map and select black&white fill (I also added a bit brightness). Adjustment layer should be on top of all other layers.

Result:

2) Delete some frames. For example, every third. Don’t forget to change the frame delay in animation. I switched it to 0.12

Result:

That’s all, I guess.
If you have any questions, feel free to drop me a message.