I'm still getting used to MOO and I'm not sure how invading planets works. If someone could explain it I'd appreciate it, thanks.

Select the planet you want to invade FROM, click the "transport" button, then click on the planet you want to invade. Then you can select how many troops to send to do the invasion.

I have just looked at MOO for a few moments so this is a help, thanks.

Also be careful of who you invade: if the colony is occupied by the Bulrathi, it will be extremely tough to capture it, even if you have both technological and numerical superiority (within limits, of course). On the other hand, if you play as a Bulrathi, you should alway try to invade a colony, even if you don't have a numerical advantage, since as a race they are that good at ground combat.

Ok thanks for the tips

MOO 1 is one of my all time favorite games, welcome to a true classic- a few notes that may help
try to soften up the planet by gaining space superiority (ie knock out their ships) and bomb a few rounds while your transports take their slow time getting there, but be careful not to kill the entire colony, your invasion force will die without an enemy base. Transport speed improves as your propulsion advances... If you have not gotten combat transports then any enemy ships in orbit are going to slaughter those transports
usually you want to attack 2:1 or so since your invasion army serves as your new colonists... you can also invade from more than one planet send transports from a number of planets, you can attack in waves or try to sync the invasion all together. This is useful if the planets you are attacking from are small in population
Planetary invasion is a good way to keep psilons, silicoids and a number of other races in check
Sakkras (fast birth rate) and Bulrathis (ahnd to hand) should use invasion as a key military component
have fun!

Also make good use of your research and spy network. Best to know what ground combat tech your enemies have ahead of time and maybe steal some of their technology to make it a more even fight.
Also, research Hand Lasers at your first opportunity to make early-game invasions TONS easier.

Also, don't forget to increase your ecology of the planet your troops are coming from to quickly replenish the population.
If I could I would sent at least twice the number of troops then the planet could handle, since a large percentage would die in battle. I would send even more if they had a strong missile defense I would really increase the numbers since most of the transports would be shot down before landing. There were a few cases I sent in 100 million (billion?) troops in order to capture a a planet that could hold 10 mill/bill. Then I would max the ecology to get maximum growth rate. My friends and I refereed to this strategy as "Sending in the Clones."