Ok....
You launch the ship, and you have to wait for it to reach Alpha Centauri, the Tech victory is only if you MAKE IT to Alpha Centauri, not if you just launch your ship. So, there has to be a way to stop you, right? That would only be fair. So, if you're capital gets taken over, then your ship is stopped or something.
Well, it doesn't matter what you're going after, all the comps will go to war with you. They'll friggin' change governments just to do it. If you start building the world bank, if you start building the united nations, if you start taking over capitals or taking out Civs, if you launch a spaceship. Each way, there's a way to stop you, and the enemy will start a war with you once you start winning that way. Why? THEY DON"T WANT YOU TO WIN.
So, by launching, your enemies will start to declare war on you of course. They don't want you to win, so they'll start attacking you and amassing armies to fight you and start taking over cities in order to take your capital in order to stop your ship.
Well, after you launch, you can only wait. You can't speed it up after it launched or slow it down. So, you can either scrap all your other cities and protect your capital only, or you can protect all cities like normal, and hope that your enemies can't break through the defenses.
I have the 360 version, so if you have that, just press the back button (to the left of the power button, not the B button) and it'll give a list of things you can do. You look down the list, and you'll see "Space Station Report". Go to that, and select it. It'll show the spaceship flying, but look on the sides and somewhere it'll tell you how long it'll be before it reaches there. Or at least, how long it'll take from when you launched.
Once it makes it, you win. But, that's if it makes it. Defend your capital, and if they have a nuke, get an SDI defense. You don't want your capital getting taken to size 1 and having no defense in it and then having your enemies just land some troops near it and taking you over.
So, in short: WAIT and DEFEND YOUR CAPITAL.
Remember, if they take your other cities, you're fine. They won't change whether the ship makes it or not.