BEGIN AT THE BEGINNING

     This post is about cadence and gear selection, so it really isn't for beginners.  It assumes you are properly fitted, clipped in, and know how to shift both front and back derailleurs.  I see too many folks not enjoying their ride because they are working too hard in the wrong gear.  Recently I saw a lady bouncing in her saddle, going about 110 rpm to achieve 14 mph on flat ground.  It was painful to watch, but since I was a guest in this group ride, I didn't give any instructions.  I am not an expert, but I am experienced.
     Let's start with cadence.  I'll use the term "base cadence" to mean whatever cadence feels good to you and you feel like you could do it for hours.  This should be somewhere between 80 and 90 rpm.  90 is preferred and if you can do that without getting winded, do it.  I'm more comfortable at 80-84.  You want to apply the least amount of pressure necessary to keep up.  Pounding a large gear for an extended period of time will make your knees unhappy.  Let's assume a base cadence of 80 rpm for the remainder of this post.  The ride becomes quite simple: choose a gear that gives you the proper speed at 80 rpm.
     Of course, on a group ride you go up and down hills, slow down and speed up, maybe stop for traffic devices.  So your cadence will vary, as will your gears.  So you do what is necessary, then drop back to your base.  Now for gear selection.
     Assume a ten speed sprocket and two chain rings.  You want to live in the middle four (for eleven speed, the middle five; for nine speed, still the middle four).    If I'm cruising in the 14-18 mph range, I'm in the small chain ring.  If it's 18 mph and up, I'm in the big ring.  It might be crossing your mind why you have all these gears and only use four.  Of course you use all of them!  Read on.
     Besides talking to your buddy or planning the next meal, you need to pay attention to your surroundings.  If you have a small, short rise coming up, assess how many gears you need to get up and over, plus what the ride leader will be doing.  If you only need one or two additional gears, stay in your chain ring and shift the cassette.  But what if after the climb there is a drop?  Then, if you are in the small ring, you should go to the big ring plus whatever cassette in the back will keep you with the group.  And yes, your cadence will need to adjust.  But don't shift too soon.  You don't want to go from 80 to 110 rpm.
     Now is a good time to mention those who are in love with their big ring.  By that I mean those who stay in it until they run out of sprocket in the back and then shift to the small ring.  Two things: it is bad for your chain (called cross-chaining) and it drops you too much in the gearing, making your rpm's accelerate too fast.  If you spend most of your time in the big ring, don't use it in the last two sprockets.  Back to the illustrations.
     So now you're cruising along and a long climb looms.  You've done this before (or not) and assess the need for four or more gears before getting to the top.  If you're in the small ring, you just keep shifting as needed.  In the big ring you have a choice: shift to the small ring now and then keep shifting the gears.  Or, shift up to the third from the top gear, then when the time comes, go to the small ring.  Here's a rule of thumb: going from big ring to small equals about two gears (really about two and a half).  If you need two gears in a hurry, and maybe a third shortly after, then the sooner you go to the small ring the better.
     Let's mention an exception: going downhill (not coasting) or with the wind at your back.  Since gravity or the wind is doing some of the work, pick a big gear and less cadence.  This is an opportunity to relax.
     There is more to it than this, but it's a good start.  I think I mixed cassettes and sprockets, pay no attention.