Playing Spaceward Ho! is simple (just like life, right?). Starting a new game gives you a few options: number of stars in the galaxy (i.e. how long the game will take), galaxy shape (can change the difficulty), number of opponents, and opponent skill level. You start out with one planet, fully terraformed, some metal, and more yet to mine. You can either use predefined ship types with various attributes, or create your own, tailoring them to your fondest desires (up to the level of technology that you currently possess). Once you've built your first ship, it's a simple matter to send it to a neighboring planet. Select the fleet that you wish to send out from the "Fleet" windoid, click on the home planet in the starmap window, drag to the destination, and you're off.
Once you've reached a planet, you either set up a colony or simply scout the planet (depending on the type of ship you sent). Colonies serve one very important purpose (besides generating money): they are the only way to refuel ships. More often then not, I'll send a scout ship out to his full range and he'll be stranded there. C'est la vie. Planets with a gravity between .5G and 2.0G will eventually become prospering colonies, given sufficient money. Planets outside that range can be temporarily colonized for strip-mining purposes, but no amount of money will allow it to be terraformed permanently.
As you pour money into your colonies and technology, you build bigger ships, better ships, and even more ships. You colonize more and more planets. Invariably, you'll run into one of your opponents (or they'll run into you). The battle sequences bring up pictures of the opposing fleets and you can sit and watch the damage rack up against each ship (the ship pictures in themselves are amusing - especially at high tech levels). After the first few times, this quickly becomes tedious and you can hit "Skip" or turn off the option. Even if you skip the graphics, though, there will be a lengthy summary in the report windoid telling of the battle, number of ships, relative strengths, etc. Once you've taken a planet, you can then start terraforming your new acquisition to your own needs. If an opponent takes one of your planets, not only will they wipe out the existing population, but they'll also start terraforming it to their needs, reversing all the time that you spent, so you want to take it back quickly.
Another nice feature, though I'm not so sure that it isn't cheating, is that you can monitor the other player's progress via a "Compare Players" menu command. Selecting that will give you the splashdown on where you stand the current relative rankings, i.e., are you 1st in weapons, 3rd in shields, 5th in number of planets owned, etc. So, if you're merrily strolling along and then check your status and find you're dead last in technology, you'd better start devoting money to technology spending. I suppose that "Compare Players" is more or less the same idea as the CIA (though more accurate), when you get right down to it.