Welcome to the forums apaulex.
This process of making your videos play on your stand alone dvd player could be very simple if your dvd player can handle avi files, and if the avi files are encoded properly. Many newer players can use avi files that use the xvid or divx codecs. You'll have to check your manual to see if yours is one of these.
To examine the avi files, you can use a program called MediaInfo. It will show you the codecs used in the files, for both audio and video. MediaInfo is free to download and use.
Assuming the player can handle avi files, and your files are using the correct codecs, all you have to do is burn as simple data files with Nero. Just like you would burn any other data to a dvd. Your player will recognize them and give you a list of files on the disk to chose from.
Now, assuming your player can't handle these files, you'll have to convert to dvd-video format. You can do this in NeroVision. You should be aware that converting an avi to dvd-video generally means the size of the video will greatly increase. The mpeg2 codec used in dvd-video isn't as good for compression as many others used in avi files.
Just start NeroVision, add an avi file or two, make a menu and let it process the files. How many you add depends on running time of the videos, I'd keep the total time down to a couple of hours if possible.
There are other programs that can convert for you, including a couple of free ones that can use a very high quality encoder called HCenc. These programs are AVStoDVD and FAVC. Either one is simple to use and will produce a finished dvd ready to burn. They can also use a free burning program called ImgBurn automatically if you have it installed.
If you use AVStoDVD or FAVC, make sure to set the output dvd-video to match your country's standard for dvds. Most of the world uses PAL video standards. The US uses NTSC. You may have to look for this setting in NeroVision as well.
Burn your disk at a moderate speed...say 8x or 12x for 16x rated disks. Use good media. We recommend Verbatim as a safe choice in disks, and they are fairly easy to find. Sony might make a good substitute if you can't find Verbatim.