I've looked through the entire manual, I've searched the various screens but I don't see how to take a warrior, for example, and upgrade him to an axeman, or a horseman to a knight. What are the mechanics of doing this?

I think the unit has to be in a city with a barracks in it. You need the required techs of course, and it costs a bunch of gold. But the icon will still be there even if you can't afford it.

Select a unit in a town (barracks are not required any more, though they may make the upgrade cheaper)

In the center at the bottom where all the command options are (fortify, disband etc..) you will see other unit profiles. Sometime more than one.

Archers can upgrade to longbow or crossbow: assuming you have the required techs/resources.

I also think it is way too expensive. Archer to crossbow was 160 gold! Ouch!

You don't even need to be in a city IIRC.

First you need to have the techs, two the resources (if needed) three the money.

Then when the unit is selected you will see among the actions buttons some buttons that look like units, these are the possible upgrades. Click them and ... done !
If there are some but greyed it is either lack or resources or lack of gold.

Hello Friends,
I have a question. When I hover over the upgrade icon of an unit, it says 160 gold. Is this just the upgrade cost of that one unit or the upgrade cost of all units of that type?

It's the one unit.

If you mouse off the icon, then hold ALT and mouse over it again, it should show you the cost for all (at least as of last patch).

Doesn't have to be in a city - it can be anywhere in your cultural borders (as of last patch - haven't played new one yet)

Doesn't have to be in a city - it can be anywhere in your cultural borders (as of last patch - haven't played new one yet)

As long as it's on a road if it requires a particular resource.

Hello Friends,
I have a question. When I hover over the upgrade icon of an unit, it says 160 gold. Is this just the upgrade cost of that one unit or the upgrade cost of all units of that type?

Just the one. If you want to see the cost for all units, you have to roll over the icon while pressing the Alt button. Pressing the Alt button while clicking on the icon is also how you upgrade all your units of that type, provided you have enough gold for them all.