No laughing here; asking questions is how you learn.
Many DVD players can indeed record on a blank disc. There used to be a number of different formats that these discs came in: CD-R, CD-RW, DVD-R, DVD-RW, and DVD+R and DVD+RW. Though they look physically identical, they work with different technologies--similar to VHS and Betamax.
Don't sweat this too much. Most DVD players that were made in the last decade and can record on blank discs, can use any of the aforementioned formats. Likely, whatever disc you have will probably work. If you are going to buy discs, DVD+R and DVD+RW are the newest, and most commonly used formats. The 'R' means recordable (record once, and it's there permanently), and the 'RW' means rewriteable, which can be recorded and then overwritten later, like a VHS tape. It is usually simpler and more cost-effective to use DVD+R discs.
If your DVD player can record on a blank disc (look for clues such as a DVD+R or DVD+RW logo written on the machine), it can record to blank discs just like a VCR can record on a VHS tape. But, just like a VCR, it is only a recording device. It needs a source such as a camera or a TV in order to record video.
To record yourself, you will need a camera or camcorder. Most modern cameras and camcorders record video (and/or pictures) to a small card that fits inside the camera. This means that if you have a camera or camcorder, you can record yourself without using your DVD player at all. That means you can take the camera outside, on vacation, or wherever; you don't have to be in your living room, and the camera doesn't have to be wired to your DVD player.
Cameras and camcorders are very inexpensive these days. You can probably find one to suit your needs in the $50-100 range, although it is possible to spend much more. Even inexpensive cameras take very good video footage these days, and using them is fairly straightforward. If you need to get the video off of the electronic card that these cameras use, and onto a DVD, the easiest thing to do is bring it to an electronics store (Best Buy or similar). The guys there do this all the time, and they'll be happy to make as many DVD copies as you need, for a nominal fee--probably in the $20 range.
You can also do this yourself, by connecting your camera to a computer. This can get a bit complicated, but it's not too terrible. If you have somebody that knows a bit about computers, they can show you how to do it.