It took some practice, but eventually I got the hang of it. I did do something stupid once in the first week, which was put it in backwards. It floated around and it hurt for a few hours. After a while my eye doc would just do a quick fitting of a new lens and trust me to know if there was something wrong, because I demonstrated that I could handle them and would take them out if there was any issue.
I preferred regular (not 1-day) disposable lenses. Pretty much all the lenses I used were rated for up to 7 days of continuous wear or 14 days if cleaned and disinfected. Some silicone hydrogels were rated for 30 days of continuous wear or 30 individual days if cleaned and disinfected. I got pretty good at taking them out. If it was the last day of a lens that I was going to toss, I would just remove it without even cleaning my hands.
I would never sleep overnight with any contact lenses, but all my eye docs said it was OK if I took a nap in them. Often I'd do that since it would have been a pain to take them out (and clean/disinfect) for just an hour, and they typically wouldn't be ready. There was an alcohol based cleaner/disinfectant system (Ciba QuickCare) that was supposed to be ready in 5 minutes though. The cleaner were thick, soapy drops that smelled of alcohol. Once cleaned, it was just a matter of rinsing in their "finishing solution" which was a special saline. I heard that it was just a relabelled combination of Miraflow cleaner and SoftWear saline - both which are no longer on the market.
Another thing my eye doc recommended was that if it was getting especially dry (I have really dry eyes wearing contacts) that I should just wash/dry my hands, remove them, squirt saline on them, and put them back in. I don't know if all eye docs think it's OK, but my eye doc thought it was fine. I've heard of some people doing stuff that just sounds wrong, like taking them out with dirty hands and spitting saliva on them before reinserting.