Ugh, I did the same thing a month or two ago when I wanted to make one little .gif. :/
This is how I use Jasc. Keep in mind that Jasc only works for .avi...at least that's how I remember it. It also helps if you have a program that can trim an .avi, because if you a really long video then it's a pain to figure out the frame range that the particular section you want is in. I use SolveigMM AVI Trimmer for that, it's a fairly easy to use freeware program, but it only lets me trim my files down so much. That causes a small amount of removing access frames later on.
Anyway, I open up Jasc, and import the file. (File > Open > (pic the .avi you're using)
The first thing you want to do is click on the bubble that says "Frames", unless you have reduced the .avi to a really small size. (Which might not be the case if you use the program I use) All my computer can handle is around 500~600 frames at a time, otherwise it takes forever to load. If you're doing something from an anime/cartoon etc., you might want to choose the "Take one sample for every" bubble, and move that to 3. I forget what that does, but it's good. Make sure you leave the "Merge Identical Frames into One" check on.
Your file opens up. Remove any frames you don't want, and then ctrl+a to select all the frames. Go to; Animation > Frame Properties. This is where you might have to mess around a bit. The higher number (display time) you choose, the slower the animation will move. Choose a number and then click OK or whatever it says. To check how smooth the animation is, click on the "view animation" button on the top. Fix the the display time according to how you want the final product to move.
After that, go to; Animation > Resize Animation. Change the dimension to whatever you want them, just remember that it's better to have a big one since you can always just reduce it in size if it needs to be done. Click OK, and then view your animation to see how it looks. You can fix the display time if needed, etc. Once you're done, go; File > Save As. Use the dropdown arrow to choose .gif as the export.
Tah-dah?
Feel free to message me if you still need help.