Ok here is the simple explanation.
You get a little disk (maybe 4" diameter)with a plug and thermometer. You set the alarm for whatever time you want to take your temp. You can temp for 3 hours before or 3 hours after this set time (a little thermometer symbol lights up when you are good to go). The ladycomp then registers the temp and gives you a green, red or yellow light depending on where you are in your cycle. Green means you are not fertile, red means you are fertile and yellow means it is learning (the yellow lights don't happen much after you establish a few cycles). If all 3 lights are flashing then you are pregnant.
If you are TTC, you DTD on red days. If you are TTA you use a back up method or abstain on red days.
When you are expected to get your period it will flash the M for AF and you hit + if you got it or - if you did not. Once you get AF, the cycle starts again.
It stores all your info and will give you averages of O date, temp shift, etc.
You can also scroll back and view past days whenever you want. You can scroll forward 6 days so you can see if it is predicting you to become fertile in the next few days. Even if you are to become fertile soon, it's still safe to DTD on green days. It builds in the extra red days to avoid a pregnancy.
This company has compiled data from thousands and thousands of cycles and I think it is as accurate as the pill % wise.
A caution....if you have irregular cycles, you WILL get mostly red lights.
I used it for TTA and TTC. Worked great both ways.
ETA: The customer service at naturalmethods is AMAZING. Those ladies are so helpful. I called just a few months ago (2 years after buying the product) and they were still helpful and sent a bunch of links for info I was looking into.