Random stuff from me, basically the cliff note version of what I teach my students the years I do a high school photography class. (some of this might have already been talked about above, but I'm lazy and didn't read all of it.)
ISO-these days, it's essentially how sensitive you want the sensor to be. High ISO=very sensitive, which is great in low light, but it also makes for more noise.
Aperture-the higher the number, the more of the photo is in focus. (i.e.-depth of field). But with how physics works, to get more of the photo in focus, the hole needs to be smaller, which means less light is let in.
Shutter speed-self explanatory. Slower means lets in more light, but things blur, because they have time to move before the hole closes. You shouldn't ever go below 1/60, unless you are using a tripod.
There is a thing photographers refer to as the triangle, which is essentially the three items above, and how they interact with each other. I won't get into it, though.
Shoot in JPEG. (RAW is really for pros. Amateurs that aren't printing the photos shouldn't even worry about it.)
If you aren't objectionable to a bit of adult language, there is a GREAT site I can message you that is very easy to understand and very informative.
DSLRs can be used just like your point and shoot, with a bit more control of focusing, and you can take multiple pictures in a row pretty quickly.
Ok, /random rambling from me.