Stumbly your cats are BEAUTIFUL!
Just you called?
I have had two laps. You will get four cuts. One in your belly button, two either side (towards your hips) and one on your bikini line. They stick a camera in one, a gas tube in another (to inflate your abdomen with CO2 so they have more room and then tools in the others. Slowly they explore your abdomen, and remove anything that is where it shouldn't be and clear things out.
You'll come round from GA and be wheeled to a ward, where hopefully you can mobilise and go home that day. You will be catheterised but they'll put it in and take it out whilst you're under, so you just get the ghostly feeling of needing a wee for a while.
Healing wise, you're looking at 1-2 weeks off work depending on how active your job is. (Office = 1 week, teacher, doctor, labourer =2 weeks)
I had to get antiseptic cream to help my belly button cut heal the first time but otherwise all cuts healed fine. Very faint scars, about 1cm long each.
I had two as it was for endometriosis, 2010 and 2014. Will prob have another at some point or a hysterectomy A lot of endo patients save them up until they want to concieve, as the success rate is pretty high in that regard. (If your endo is preventing conception that is.)
DFriend had one as a "fertility investigation" after 3+ years with no luck. She had hoped they would find sonething like endo to aid their case for IVF and was gutted when they said there was nothing wrong. And then fell pregnant the next cycle. 
Any specific questions, let me know!