Welcome to Frozen Synapse.  Here are some brief instructions to help you get into the game.  The "Help!" tab at the top right also gives some useful hints.  Don't bother reading this if you don't want to.

First, the mission objective.  The team on the left (Offense) is trying to get as far to the right as possible within fifteen seconds.  The team on the right (Defense) is trying to stop them.  You can tell which side you're on because the units have your name printed next to them.

What you're doing when you're playing Synapse is basically designing a plan which your units carry out during the fifteen seconds of game "execution" time.  Your opponent is doing the same, and when you have both have finished you see the plans go against each other.

The time controls at the bottom of the screen let you test out your plan, and you can also give a plan to your opponents' units in order to see how yours would fare against it.  Use the space bar to play and pause the simulation.

In general, you select units and plan elements with left click, add waypoints with right click, and bring up the orders menu with middle click.

To delete plans, you can use backspace to delete from the end of the plan, or the delete key to remoe a selected plan element.

When you're happy with your plan, open the tab at the top left of the screen (the Endplay Menu) and hit submit.  You will then load your opponent and will see how you did.

Games of Synapse with one unit each are very different from games with more than one easy (say 2v2 or 4v4), and I find they're good for different moods.  Make sure to try out both kinds.

If you don't like the look of an endplay, just click on "Next Level" in the Endplay menu.