The beginning can be difficult, although I've never seen something quite as extreme as what you describe. A couple things that might help:
1. Ctrl-N until you get an starting place you like. If you want an easier beginning game, wait until you get a home planet with good production bonus tiles.
2. Buy a factory on your home planet on your first turn. Maybe one on the second, too.
3. Go to the Domestic Policy tab and set your spending allocation to 100%. Think about what to set your military, social, and research sliders to, as well. There are many theories about the best settings for the beginning. But spending allocation to 100% on the first turn is an absolute must (it should start here by default, imho).
3. Some races start with better engine technology or with a miniaturization bonus, which can make a difference. Try playing one of these to get better colony ships.
4. You must design your own ships to play GalCiv2; the alternative is not practicable. On your first turn, design a cargo-hull ship with the colony module and as much engine power as possible; just double (or right?) click the components to add them, it doesn't have to be pretty. This colony ship will be faster than the default model and will help you in the land-grab race.
5. Auto-survey is ok, but it isn't ideal. During the colonization period, your flagship's primary mission is to scout for good planets, and grabbing anomalies is secondary (but still important).
6. Start the game in cheat mode and hit Ctrl-U (I think?) to reveal the map. This might show you what the AI is doing to get ahead.

Good luck!

And just because the AI grabs a fwe more planets than you doesn't mean that the game is over and impossibly difficult. Build some offensive ships, research planetary invasion, you know. . . .

Although I really find it hard to believe that the AI got 14 colonies before you got one, got a saved game or pictures of that? I am guessing you got a really, really bad starting position. In that case, just remake the game.

Terrans have high skill points but weak starting techs.

In game terms, crap early, better later.

I think its a beginners mistake to try and buy those colony ships.

To do so on large/huge galaxies is quite silly. After all, you start with 5000 and at most you can buy 4 or 5 ships and then it's finished.

What you should do instead, especially on those larger galaxies, is to first built a research lab, and tech-rush speed upgrades, possibly up to impulse drive. If you have Ion's you can make ships that go 4 units, if you research impulse, you can make your colony ships go a whopping 6 moves a turn.

Simultaneously, buy a couple of factories, maximize your industrial capacity and tax revenue, and spent it all on millitary. Just buy only factories! No ships.

If you do this, and buy a couple of factories on 2 or 3 worlds, by game turn 6 or 7 you are churning out 1 colony ship per turn average

But its very important not to get your hopes down! On my first games I found the AI overwhelming too, but after you get the hang of it and follow a few common sense guidelines, you'll find yourself smiling at beating down those AI's

It is true that the "normal" level seems very hard at the beginning. On the other hand, it can be quite easy, once you start designing your own ships. Here is a strategy I found useful at with small maps at "normal" level:

- Specialize your homeworld to trade and built some Trade Centers. This allows to buy a lot of useful things each turn
.
- Design your own fast explorers and colony ships. Remember that you can build in multiple life supports to enhance the range and several drives to enhance speed. Use Transport hulls, for you don't need armor with that kind of ships. So you have plenty of space for enhancements. Ships with great range allow you to colonize systems that yout opponents cannot even reach - a effective strategy at this level.

- Colonize sone additional planets and specialize them for manufacturing and research. Always add a entertainment center and set your tax rate to an amount that provides your citicens with 100% content. That gives an immense growth bonus - so your colonies will grow rapidly.

- Use constructors to build influence bases that will help you create an united cultural sphere. Research gives them great influence later in the game.

- Build some strong ships very soon to protect each of your planets. That should prevent evil races from trying to eradicate you early in the game.

- With that strategy should soon have a much greater population and research than your opponents. Just use all your influence ressources, research the corresponding technologies - and a cultural victory is easily archieved (a little too easy, maybe).