I have Sporty's IFR dvd course, and have been having a hell of a time keeping things straight in the "Terminal Operations" section. I am keeping notes, but it's still scattered in my mind. I'll write down that "LDA's are offset from the rwy by more than 3* (or some angle, I forget) and may or may not have a glideslope", but I don't see how it fits into the whole set of approaches.
LDA is basically an ILS or LOC where the final approach course is more then 3 degrees off the runway centerline. I'm not sure why the FAA felt the need to create that different name -- perhaps it has to do with ICAO standards. From a pilot's perspective, an LDA is the same as a LOC (and a LDA with GS is the same as an ILS) except you're going to have to look left or right to see the runway when you break out and make a heading correction to align yourself with the runway.
I understand there are precision and non-precision approaches, but not which ones fall into those categories, or what the real difference is (precision has glideslope? Is that the only difference?)
That's correct -- precision has an electronic glide path, and nonprecision does not. The joker in the pack is the RNAV(GPS) approach with LPV (that's "localizer precision with vertical guidance"), which requires a WAAS GPS. LPV has a GPS-derived precision glide path, and is treated as a precision approach for training and testing purposes, but as a nonprecision approach for alternate minimums purposes. There is also something called LNAV/VNAV, which is treated the same as a LPV. LNAV/VNAV uses barometric data to aid the vertical guidance, but you're not likely to see that one in a light single.
The other big difference between precision and nonprecision is how you determine the missed approach point. For precision approaches, there is a Decision Altitude (DA). You fly the glide slope to the DA, looking for the runway as you descend. If you reach DA without having seen the runway, you start your missed approach upon reaching DA. Nonprecision approaches have a Minimum Descent Altitude (MDA), and a designated missed approach point (MAP) which is determined either by time from the FAF, DME distance, or passage of a ground navaid. Once you pass the FAF, you descend to the MDA, level off, and start looking for the runway. If you see the runway and are in position to descend and land, you do. If you reach the MAP without being able to land, you start the missed approach from there.
Also, are there standard minima associated with each type? There seem to be unique minima for every approach, but I keep hearing about standard and non standard minima.
The Terminal Procedures Standards (TERPS) set "standard" minima for each type of approach based on a wide range of factors, including everything from the type of system (VOR, NDB, etc) to the distance from the navaid to alignment with the runway to the lighting systems associated with the runway. That's all done by the folks who design the approach charts, it's transparent to you, and it's really not your concern -- you just use what's published and that's that.
Where you need to worry about standard vs nonstandard minimums is when you're selecting an alternate airport. Each approach to an airport is evaluated by the FAA to determine if you can use the "standard" alternate minimums to decide if the forecast weather there is good enough for you to use that approach/airport as your filed alternate, or whether you must use nonstandard minimums based on some criteria in TERPS. The standard alternate minimums are 600-2 for precision approaches, and 800-2 for nonprecision. If there is a reason those aren't good enough, then that approach chart will be marked with a triangle-A symbol to tell you to look in the nonstandard alternate minimums section of the approach book to see what the nonstanards alternate minimums are for that approach. If that approach is marked A-NA, you can't use that approach to file that airport as an alternate.
