I use 3 different programs to do this:
Hamster Video converter ( I get most of my videos from youtube which is .FLV and need converted to .AVI or .MPEG )
VirtualDub ( This is the program you will use to "cut" or crop selected parts of a video ) - Note: Ive had countless problems with this program from "Unrecognizeable File Type" errors and "Unable to load program" errors ... its annoying, but I havent found a better solution yet.
Photoshop ( You will open the cropped video in photoshop and saved it as a .gif32 or .gif64 )
Once you have it converted and cropped. Open it in PS. You probably will want to shrink the video's dimensions down or you will have a .gif that is like 10 - 100 MB. That is simply too big.
To shrink the dimensions, you can use the crop tool or go to Image -> Image Size -> and Adjust the HxW . You will need to convert it to a smart object, so click "Yes".
Now that the video is shrunk down, go to File -> Save As -> Web n Devices . In here, you want to set it to "Loop Forever" and either .gif32 , .gif64, or create your own settings. Try to get the highest quality settings without topping like 2 - 4MB . Anything over 4MB might take forever to load.