Double-click on the Xconq icon. You get an initial screen with several buttons. Click on New. You get a list of available games. The "Introductory" game should be highlighted; if not, then find it in the list and click on it. Then click OK. You then get a list of sides and players; click OK again. After some activity, you see several windows open up.
The most important window is the map. It's mostly black, indicating that you don't know anything about what's out there. You should see a small picture of a city, and a small picture of a diagonal line of soldiers below it; the soldiers have a heavy black outline around them. This means that they are ready to move. Note that the cursor is a arrow, and that it always points away from the soldiers. This means that if you click anywhere in the map, the soldiers (your "infantry unit") will try to move to the place you clicked. This happens the same whether you click in an adjacent hex (or "cell") or one far away, or even somewhere out in unknown regions. Your infantry is smart enough to find its way around some obstacles, and will stop and wait for new orders if they are blocked.
Click to move the infantry a few times. Notice that the turn number is changing at each move. Then all of a sudden Xconq will highlight a new infantry! Your city was working on it quietly while you were moving the first one; now Xconq will ping-pong between the two, asking first about one, then the other. Get used to it - it won't be long before you have dozens or even hundreds of units at your command! Fortunately for your sanity, Xconq provides some assistance - more on that later.
At this point you should have several infantry wandering around. Use them to explore the world - send each out in a different direction so as to learn the most the fastest. Eventually they will have spread out so much that Xconq has to scroll over to each one before asking about it. This can be a little disorienting. One thing you can do is to go to a lower magnification for the map; either click on the small mountains picture in the lower corner of the map window, or go to the "View" menu and pick something from "Set Mag". With a little experimentation, you will see that you can magnify so much that a single hex nearly fills the window, or make the whole world appear to be the size of a postage stamp.
Sooner or later you will encounter either an independent city or an enemy unit of some sort. You can tell which is which by looking at the emblem in the upper right of the unit; independents have nothing, while enemies have a small "2". To attack either, just click to move your infantry into the other unit's cell. There will be a bit of flashing, and then either nothing happens, your infantry disappears, the other unit disappears, or if a city, it changes to be on your side. In the last case, you have just captured your first city!
Capturing cities is good, because you can then have them build more units for you. When the city is ready to start building, it will be selected just like your mobile units; select "Build" from the "Play" menu, which then brings up the construction window. Click on a type of unit (on the right side list), then "Construct"; this tells the city to produce units of that type, as many as is indicated by the little text box in the upper right corner. You can choose to build more infantry, or you can choose armor, which takes longer to build but moves twice as fast (except in the mountains).
Building units and spreading them across the world is what this game is all about; you win when the enemy side has been entirely captured or eliminated. If it's being run by the computer's AI, it may just resign if hopelessly outnumbered. You should try to capture the enemy cities whenever possible; even if it is immediately recaptured, the disruption works in your favor.
You will probably discover that when you have a large number of units, you get traffic jams because units can't move through each other. This is because the intro game does not allow "stacking", for simplicity. Most of the regular Xconq games do allow stacking.
When you're comfortable with how to play Xconq, you're ready to play the standard game.