In short, the best way to increase population faster is to have high morale. AT 100% you get double the growth rate, at 75% its something like 1.5 x normal rate and at 41% its normal. Below 41% morale theres no growth and below 21% you lose population. This rate is per planet. The Torian superability gives a much higher growth rate for 100% approval. But you'd have to stay at that level. Keep an eye on those thresholds.
Remeber that the growth rate is based partly on the current population, so the more people you have the faster they will increase in numbers.
You can build fertility clinics (I always do on newly conquored worlds) butthats beyond the colony rush phase.
Then theres the bonuses you get just from researching Fertility Acceleration and ummm the other one thats with it. The first one is not all that hard to get early. Somewhere around 6-7 weeks, depending on your sliders and research ability.
Lastly, you can take population growth as a bonus in the galaxy set up before you start a game.