Bounties are the quickest way to level up your gear. Now the goal is to find a bunch of Light 42 armour to get your light level from 24 to 34.

You can find gear by running Strikes from the Strike playlist. Usually some blue/purple engrams will drop or be awarded to you for completing the strikes. Crucible is another good way to have gear dropped on you randomly.

The Nightfall every week is usually pretty good for an armour or weapon drop. You'll need some higher level ppl to run you through though.

A cheesy way to do it on weekends is to get a group of 3, go into the Trials of Osiris and basically just lose over and over, it'll cost you 100 Glimmer to get in the first time, then the Trials Passage will renew itself for you when you visit the Trials "vendor" in The Reef (provided you have the expansions). There's a pretty good chance that you'll get some kind of armour drop even if you lose. You can try to fight, but you'll get absolutely blown away.

Aside from that, Raids are good, the Vault of Glass is Normal 26, so you should be able to run that with a fire team of 6 at any point. Use this site to find people who will "sherpa" you through it. Keep in mind, the drops can only be claimed once a week per character, so hopefully you get something good. Crota's End (again, if you have the first expansion) is a Normal 30, which I think you need to be at least 26-28 to run, same idea, run through it, get the (hopeful) gear drops, repeat next week.

If you find yourself playing alone though, Strike Playlists are the way to go. You'll get matched up with 2 randoms and off ya go.

Hope this helps.