That was a great run-through, Dogmama. I have just one little tip to add. Before you put the new tube on, look to see if there is anything embedded in the tire that caused the flat in the first place. I always carry a small rag with me and I rub the inside of the tire looking for anything sharp. (Remember that there can be more than one!).
When you take the old tube out, try to remember which way it was oriented. Blow it up a little and see if you can see where the hole is. Picture your tire like a clock. Put the stem in the 12:00 position. If you see that the hole is at the 4:00 position on the tube, look at the 4:00 position on the inside of the tire. Be careful because that sharp object could cut your hand. I flatted once while mountain biking, and the culprit was a tooth from something like a rabbit!!
Sometimes whatever flatted you doesn’t stay in the tire. But if it does and you don’t find it, it’ll flat your new tube, too.Oh, and I can't stress enough how important it is to practice at home before you need this skill out on the road/trail! You can practice, pray it never happens or walk home!