capture units an ships

To capture ships you need to have reserched ship capture and need to put boarding party components on the ship which is going to atempt the capture. I would also advise shield depleating weapons since you cant board a ship with them up, and to use them only on ships which have been cripled by ion mines.

To capture planets you need to have built troops and or fighters and put them on board an armoured freighter. You then give this ship capture planet orders and send it at an enamy planet. Its a good idea to excort these ships with combat ships to deal with enamy ships saterlites and weapons platforms.

Once landed there will be ground combat betwean your forces and any defenders win that and you have the planet.

A troop transport is just a ship with cargo capacity holding troops this is usually a freighter but you can do it with any hull. You have to give the ship capture the planet orders either as its strategy or in the tactical battle there is a button with troops on it which gives the order to do this. You can do troop landings from almost the start of the game in stock.

To get boarding parties and security stations you need to research Military science till you get advanced military science and then advanced military science to get boarding parties etc. So that will take some what longer.

It actually can be on any hull, but you do want the fastest vessel possible, and depending on the size vessel you are trying to capture, you want the largest amount of boarders possible.