I've recently gotten into this game and would like to know some of the efficient ways to transfer installations to other planets for colonies as my way is taking a long time and the civilian shipping lines are doing nothing even when I have things set up for them.
One thing to note, particularly early on in your game. It takes a long time to move significant quantities of installations between planets. As your engine tech and number of cargo ships increase the time drops but it will still take many in game years to transfer sufficient installations to be particularly useful.
You really have three options for getting facilities to new colonies.
Use your own freighters to transport them from one of your main colonies to the new colony. This can be slow dependant on how many freighters you have built and their cargo capacity, and costs you fuel, but it is fully under your control. Most installations you will want to move early on take one standard cargo bay each to transport, if you are using freighters with small cargo bays they will only transfer fractional amounts of an installation on each trip.
Use the civilian shipping lines to transport the facilities. This doesn't cost you fuel but does cost wealth. Civilians pick their own jobs from those available so it may take time for them to decide to work on your contracts and sometimes they seem to ignore them entirely. This varies from game to game, sometimes I've had civilian freighters sitting idle while there were available contracts, other times they have prioritized my contracts to the point that they are not keeping up infrastructure deliveries to colonies halting their growth. One trick I've found that tends to help them pick your contracts more frequently is to set up multiple smaller contracts to move part of the total installations rather than a single big one. So for example, if I'm moving 100 auto-mines from Earth to Mercury, I'll set up five supply contracts for 20 auto-mines each on Earth and five demand contracts for 20 each on Mercury.
The third option for a colony with a population is to transport a number of construction factories using one of the above methods, transport some minerals(either via freighter or mass driver) and have the colony build it's own facilities. You can also do this on unpopulated worlds by training construction brigades and moving them via troop transports. This method tends to be slow as you will usually only transport a limited number of construction facilities(otherwise you would likely keep using one of the above methods) but it doesn't require you to keep your freighters transporting all the time and removes dependence on the whims of the civilians.