There are two methods, there is sync and manual. Sync is where you put all your songs in all at once BUT it will erase anything else. Manually, you go into your music library and drag the song and movies or whatever to the left column where it says (name) ipod and drop it. Then it should say it is copying to it. comment back if it doesnt work. GOOD LUCK
You need to use a video converter to convert the files to mp4 format so they can be played on your ipod.
Make sure the videos you are trying to add are on mp4 format, you can use Videora to convert them if they are avi or other format, videora is free and works great, i use it all the time, i have posted on youtube some tutorials you can check them out if you want, to give you an idea. Vidora tutorial