How would you go about returning civilization to the galaxy?
Lets assume you chose the "destroy" option, since if you chose control or synthesis you could just have the Reapers make some new relays. Also let's assume this is the real ending and the indoctrination theories are all just hot air.
There are some things that must be agreed upon prior to beginning this process. First, the Sol system is the new galactic capitol, it has to be since this is where things are starting up. Second, no more secret technologies, if galactic civilization is to be reestablished then there must be total cooperation between the species with everyone having access to everything the others have.
First thing we must accomplish is to gather and study all of the reaper technology we can. Indoctrination is no longer an issue so we shouldn't have to be too concerned about it. Reapers have FTL technology that in addition to being faster, does not require discharges or refueling. This tech is vital for galactic travel with no relays. We also need to devote lots of resources to creating as many quantum entangled pairs as possible. These would be installed on all capital ships leaving Sol, they would also carry with them as many extras as we can spare to give to colonies we establish and rediscover. Sol would act as a galactic switchboard, if a Salarian colony needed to contact an Asari colony in another part of the galaxy, it would use its communicator to contact earth then data would be locally transmitted to the communicator paired with the Asari colony.
Huge capital ships would need to be constructed to provide both transportation and long term habitation for refugees returning to their homeworlds and colonists trying to contact old colonies and establish new ones. They wouldn't need to be exceptionally powerful in battle so they wouldn't likely be as expensive as dreadnaughts, but they would still have to be able to fend off pirates or hostile colonies.
For races whose homeworld is far away, for example the Quarians, the majority of their race would be put in cry sleeper pods on the decades long voyage to Rannoch, while the few noble volunteers pilot the ships, knowing they likely won't see their home until they are old. Alternatively they could crew the fleet in shifts of 1-2 years. This would be necessary not just so that more QUarians could make it back home in good health, but so that they will have enough resources to survive the voyage.
While these ships are traveling, scientists need to be studying mass relay tech. Hopefully the Conduit, which was not connected to the Relay network, was not destroyed. Once a viable blueprint is discovered, it can be transmitted to everyone with a communicator, and eventually a new relay network can be established.