As Albeig has said you need to render your video in a format which is compressed as opposed to uncompressed.
When establishing the output settings for your render most editing softwares will give you an option to use a compression setting such as wmv
http://www.divx.com/divx/windows/converter/
gives a link to a free download for a dixv convertor tool based on the now out of date DR Divx. Many people on this forum have suggested in the past that Dr Divx does the job very nicely. I do not have this software and cannot tell you if the demo is feature limited,time limited or does something like stamp every frame of your video with "made with divx convertor demo" or similar.
The full version can also be bought from that page for £12.99 [roughly $25USD].
Once you've rendered into a compressed format you ought to find that the result is 10mb or less not the outrageous size that results from using no compression.