How to earn money for supports?

You need to get every single last hit your carry doesn't get

If he's too far away to get a last hit, take it from him. When he goes back to base or to gank, focus 100% of you attention on getting every creeps money until he returns. If neither are applicable, stack and pull, so you can make money from last hitting jungle creeps. Supports usually need to be better than carries at last hitting, imo.

You can go into the jungle and pull the jungle creeps into your lane

If you do this when your teams creeps are passing by they will start attacking the jungle creeps. They will tank the jungle for you, take the last hits. Dont do this if the enemy team is pushing. This will most likely give your team an XP and gold advantage if you do it right.

When a dying enemy creep is out of you carries range, take it if you can. Ask your carry if you can get some farm for arcane boots. its important.

Sometimes it can be advantageous if you stay in your lane whilst your teammate roams to gank somewhere else, if you are not needed. Just have a TP ready.

Also, make sure to cooperate with your other support

If you buy courier when you start, someone else should buy the wards. If you buy flying courier, someone else should buy wards etc.

Try and work out if you can farm the jungle as a support

Jakiro's Dual Breath for example could be used to farm the jungle (albeit very slowly), though you might not want to drop levels into it early on so that might not be a good idea. Crystal Maiden's Frostbite freezes jungle creeps for 10s so it could help you jungle. Sand King's Sand Storm clears camps like nothing else. Tidehunter's Anchor Smash will clear camps quickly without him taking much damage.

If you're playing a hero that has an AoE clear like  Sand King/Tidehunter it's a good idea to stack the jungle before you're 'ready' to clear (i.e. Sand King will want Sand Storm lvl 2 or 3 before clearing camps, or Tidehunter  might want  Anchor Smash slightly higher level to clear faster), so you can get a lot of gold and experience in a burst.

Ganking early can be a great idea as well if you're a strong ganker (and is also an incredibly good way to impact the early game when playing support). Just be careful that your carry isn't gonna die as soon as you leave lane (particularly if they're melee and don't have an escape), or be heavily prevented from farming.