If you only want to see the canyon from the South rim & are looking for a day or 2 there & plan only on gazing at the canyon and/or doing some light hiking as far east & west as is allowed (which isn't very far) then staying in Williams at the Grand Canyon Railway Hotel then & taking their train, as Sagebrush says above, is easiest. That saves you the long drive from Williams to the canyon & back, the waiting in line in your vehicle (sometimes for an hour or longer) at the entrance to get into the park & the park fees. The hotel that the train departs from & arrives back to daily is quite decent. Arriving at the hotel the night before, then taking the train up to the canyon & back makes for a relaxed, easy day (or longer). It's better to stay the night before because the train leaves early & they do not wait for any late customers. If you drive to the train the morning of departure, you run the risk of being ng late & missing the train which will have wasted the price of your tickets. They must be reserved ahead of departure day & there are no refunds. They have different seating locations & amenities on the train, first class to coach & you pay for what you want when you buy your tickets. The train ticket price includes all park entry fees. You can do one day up & back which will give you about 4 or 5 hours at the South rim, which is enough time to do some basic hiking along the rim, have lunch & hit the souvenir shops, or you can book overnight or longer at the Grand Hotel which is right at the South rim. The Railway has options to book your return up to several days after you arrive at the canyon. They work packages with the Grand Hotel, go to the Railway's website for what's available. You can't venture all the way down into the canyon unless you've already booked a mule trip or other guided hike which are quite involved & expensive endeavors & typically take at least a week. Also, entering down into the canyon by yourself requires permitting. It's not recommended that first timers attempt this without a guide, which must be hired & it may be the case that you cannot go down into the canyon without one. I've never done it & I believe that's the case but maybe not. I do know that you need a permit, you can't just walk down into it. Going down into the canyon is no joke & not for novices. Check the national park service's website for all the info.
But if you want to spend as much time along the rim as you want & then continue your trip on to surrounding locations such as Monument Valley (a must see for all Americans at least once in life, as the canyon is) Page, Lake Powell, etc. then you're better off driving into the park & staying at the Grand Hotel on the South rim. It's quite large & very nice. Their staff can assist you in booking whatever adventure that tickles your fancy. You're better off calling the hotel weeks ahead to inquire as to what they offer & for room rates & availability which vary depending on the season. That will mean spending big bucks, however. So for a fairly quick visit, staying in Williams at the Railway Hotel & taking their train up & back is the most hassle free. If you're seeing the canyon as part of a longer trip to others areas, driving to the park & staying at the Grand Hotel right at the rim is simplest. If you're going in the near future go soon, don't dally. It can get pretty hot up there in the Summer which is almost here, plus when school is out for the Summer the crowds really increase. I personally think the best time to go is in October or early November. It's cold enough to make it very nice but not blisteringly so & it's before the Winter snows start. Good luck & enjoy it. If you've never seen it, it's a stunning jaw dropper.