Uphill=shift down, Downhill=shift up; or how to change gears on a bicycle

On Saturday Stuart and I went for a long long ride - or so it seemed initially. In truth it was only 12 miles, but it took me 2 hours to do! Three possible explanations exist: Firstly, I kept having to stop and get off the bike at intersections as I cannot stand up and look around quickly enough, secondly I pedal too slowly, and thirdly I had no idea how to change gears so stayed in a fixed gear almost the entire way through. Eventually though, on the way back which was very much downhill, I had to stop and ask Stuart to shift up for me as it was impossible to cycle in such an easy gear.
I had my lesson with Pata on Sunday, and she had brought along a trainer. She mounted my bike on it, explained the logic of the gear changes and then got me to pedal away. Sitting on the trainer meant that I could think about the gears and shifting up and down seemed all very easy. Naturally my fear was that I could not concentrate on 2 different issues: staying on the bike and changing gear simultaneously.
However, after 15 minutes of this, we were off towards the bike path. However, we made a short stop in a parking lot where Pata showed me a more elegant way of stopping: standing up, one pedal down, braking and then stepping forward. I can sort of do this now, but I think I need to practise a bit! This is a very useful skill, as my braking and stopping skills are not quite comfortable yet.
It was a sunny day, and when we got to the bike path, there were lots of people out, enjoying themselves. I started cycling and immediately changed gear....and again....and again! Suddenly, it all clicked, and changing gears no longer had this air of mystery and apprehension surrounding it. I relaxed (as far as possible), and started enjoying myself.
In the end, it turned out to be a great ride - naturally I am still somewhat shaky both on the bike and when trying to stop, but I am still amazed at the magic of changing gears! This week I am going to practise stopping and also cornering, at which I am rather appalling. And naturally, changing gears!