Vector graphics are scalable graphics created based on geometric curves, points, etc, and typically are edited by vector based programs such as Adobe Illustrator, Corel Draw, and I guess on a very basic level, programs like Powerpoint and Microsoft word, but I’ve never used them for that purpose so I can’t speak for it. I use Illustrator to edit/create vector graphics. Examples of vector file extensions are .eps and .ai (Illustrator file).
It’s not necessary for you to use vector graphics, you can also use bitmap based imagery like jpgs. The only necessary thing for you to remember when designing your own materials is to work with high resolution graphics. Vector graphics and fonts (un-rasterized) have the benefit of scaling to any size without pixel distortion, but bitmap/pixel based graphics like photoshop brushes, photos, etc all have to be high resolution. If not, your invites will come out looking blurry when printed (officially, pixelated), even if they look right on your computer screen. Almost all images you save off the internet are small, low resolution images unless otherwise noted. I wrote a post about high vs. low resolution here in this helpful thread: http://boards.weddingbee.com/topic/fonts-fonts-and-more-fontsagh
However, you are in luck if you want to do electronic/digital Save-The-Date Cards since your Save-The-Date Cards will ONLY be displayed on the screen. It means you can work in low resolution. However, I still suggest working in high resolution because you can always save a smaller copy for the web, but you can’t make graphics bigger without degrading the quality of the image.
http://www.dafont.com is an excellent resource for free fonts. For decoration, I would recommend searching for embellishments based on the program you are using- for instance, if you are using Photoshop, try searching for Photoshop brushes to find a ton of gorgeous decorative elements you can use in that program. You can also try stock websites- I use Stock Exchange. Deviant Art is another website that offers a lot of free embellishments, check out the Resources category. Keep in mind that vector graphics cost a lot more than flattened stock jpgs. Make sure you love it before you invest in a stock vector graphic.
If you are new to working in digital “design” I would recommend playing with free graphics first before spending money on stock.
Don’t be limited by looking for just “wedding” related items, try searching for graphics/stock based on the look you want- art deco, modern, victorian, vintage, retro, reniassance, floral… whatever you want your invites/STDs to look like, you can find images that match!
It can be confusing if you are new to it, but feel free to post questions!