what effect does it cause the most during that time in one's chart?
Many like to think of it as a time of learning. I'm currently experiencing mine at the moment. Saturn has just crossed over. Life generally slows down and it's a time of introspection and we are tested by Saturn as to "what we want in life" in the next 30 years.
Some people (not all) even fall prey to chronic illnesses. You may find that a lot people say bad things about how scary the return is. It isn't necessarily painful/scary for everyone. A good example I often like to make use of to portray a case where Saturn's return proved to be exceptionally beneficial is Arnold Schwarzenegger. Arnie became very famous after the 1984 super hit Terminator 1. T1 was released and hits the cinemas around his return which granted him an emperor like status and he quickly became a household name/icon.
Does it affect the native by the house that Saturn is located in? Does it affect the native by the aspects that are made to Saturn? Does it affect the House ruler Saturn rules? Or when Saturn does return, does it have a general effect on the native?
Yes, depending on where Saturn is located in your natal chart it teach you lessons about those areas of your life where you need to focus on. The general gist is the faster to learn the lessons and the quicker you learn to accept the unacceptable, the smoother the return will go for you. You may find that if you put yourself through hell in that area of your life which Saturn affects, the return will bare fruition during the return and the results will be very favourable. You'll need to check the house placement and sign placement, besides the aspects it makes to natal, transiting and/or progressing planets.
Is there any indication(s) that you would tell a native to look for before Saturn hits? Such as what would be the most important lessons to fulfill before that time comes.
Yes one can tell when Saturn will make its return. Simply draw the chart up of the native concerned and check an ephemeris chart. The chart will tell the reader on what day and what month Saturn will return to it's natal position. E.g. I was born with Saturn @ 21 degrees Scorpio. If I were unaware as to when it would have come full circle, I'd refer to an ephemeris chart and check what date Saturn will arrive 21 degrees. You will feel the effects a few degrees either side of when Saturn comes full circle, so in terms of time, you'll feel the effects a few weeks this side and few week that side of your return. Be mindful that sometimes when Saturn is transiting your sign to make its return it, like other planets, will go retrograde and cross over it's natal position so you may have to go back and learn your lesson again.
Addendum: try and keep calm as much possible and all will be over in due course. Don't let literature and people's bad experiences get the better of you. Once your tested, Saturn will only leave you feeling stronger and tougher than ever before. So I'll say enjoy the return and learn what the lord of karma wants you to learn.