Burning (for AVIs, scroll down)
For the first question you use Disk Utility (I know - might not be your first guess) which comes with the system in /Applications/Utilities (when Finder is active, use the Go menu).
Once in Disk utility, insert the DVD, then go to the File menu -> New -> image from ds0(somethingsomething) and then choose location, file name, and CD/DVD master from the dropdown menu.
To burn it, it will appear in the list to the left under the divider under the harddisks etc. Click on it once, then click the Buirn button on the toolbar when you have inserted a blank DVD.
To burn a DVD with files, you cannot use Finder directly as that does CD-s. Instead, make a folder on your Mac, and fill it with the DVD contents, folder layout etc. Then in Disk Utility, File->New->Image from folder. NOTE! That will effectively store your data twice, so keep that in mind for disk space. When image is created you burn it as mentioned above and when your DVD seems to work you can delete the folder or the image, depending.
To burn a DVD from the applications, use the burn features within the programs. iTunes and iDVD doesn't require you to use Disk Utility.
As for 3rd party apps: I use a very popular burning program called "Roxio Toast", but there are others. Toast is a Mac burning app with a really long legacy and it has really many cool features built in, kind of what Nero was when it was still good (before it got overloaded (instead of re-loaded) with extras).
www.roxio.com
Others responding to this thread may suggest other tools that they prefer/like that may be cheaper or even free.
I got Toast and have never really used any others, so not claiming the others suck.
Finally, a really popular tool for converting movies from DVDs directly to file off of the DVD is Handbrake:
http://www.versiontracker.com/dyn/moreinfo/macosx/21117
What I usually do is play the movie 3-4 seconds, quit Apple DVD player, open Handbrake and go.
AVI videos
I am not entirely sure what you intend to do with those AVIs.
If you just want to burn a DVD with a bunch of AVIs, use any of the methods above.
If you want to burn movie DVDs of them to use in your home DVD player, then you need to convert them. Toast (mentioned above) can convert DivX movies on the fly to burn to DVD as a movie DVD.
As you might know, an AVI is (like MOV in Quicktime) really just a container of video and sound tracks that again can have different codecs inside. That is why one AVI will play in Media Player and another doesn't and it's why DivX movies before might have AVI extensions (it's a good idea to rename them to .divx).
DivX for Mac codec is here:
www.divx.com - free for playback, pay to create, trial period. Also search this forum for Xvid.
For WMV, go here:
http://www.microsoft.com/mac/products/flip4mac.mspx
That is however a limited licence. They let you watch WMV and stream on the net and watch embedded wmv amd wma <= 9 without DRM. For pay, you can get Flip4Mac Studio which lets you create/convert to/from WMV to other formats supported by Quicktime. Combine this and DivX codec above you can convert from WMV to DivX even.
As an alternative to most of the above: A really popular conversion tool for video from most formats to most other formats (including a format you can burn on DVDs) is
http://www.techspansion.com/visualhub/ - also a lot faster than QuickTime on encoding. Payware, but there is a "light version" from the same author called iSquint.
Good resources to look for apps in general that people mention is
www.versiontracker.com (my fav) and
www.macupdate.com (also really popular) as well as c|net
www.download.com
