In the online you have to first pick a faction to align yourself with and then build the clan up in numbers. For this trophy you need to hit 40 survivors in your clan. Your clan needs a certain number of supplies to remain fully healthy each day (each MP match). This number varies depending on how many people are on your clan, so you need a lot more supplies per game to keep a large clan healthy. Exceed the the target each round to make your clan grow.
You earn supplies by picking them up off of falling enemies that you either killed or assisted on the kill. Also the number of parts you earn during a MP match (basically your score for everything you do in the match) is converted to supplies at the end of a match. These are converted regardless of whether or not you spend them on mid round upgrades or ammo so feel free to spend them all.
I've found the easiest way to rack up supplies to fill your quota as a beginner is to play 'support'. After you successfully crafted three items you can gift an item to another player; this will earn you parts. I scored more parts/supplies than the top players during some matches simply by crafting and gifting stuff whenever possible.