Personally I'd want to know what they want the gold for. At your level you don't need to spend your gold on that, but on getting flying, professions, gear and the like. Looking at your guild...it's only level 4. If they're already trying to get gold out of you...find another guild. It already doesn't sound worthwhile.
To put money into your guild bank, you just click the Deposit button at the bottom of the guild bank window (doesn't matter what tab you're looking at) and you can enter the amount of money to deposit. Then hit Accept.
It's up to you whether you want to help build your guild's funds up or not. Many guilds will get donations from members to help pay for new guild tabs, fund repairs, or for officers to keep the guild bank stocked with particular supplies, especially if they are smaller guilds or just starting out. Otherwise the weekly guild activities provide plenty of money when the objective is complete. If the guild is level 5+ money is also generated through the Cash Flow perk.
If a guild requires donations to remain a member I might be a little cautious, but it depends on what my relationship with the guild is and what the guild's policies are. For instance, a guild may have a rule that you have to deposit money every so often to help pay for repairs, if you use repairs often. That might be reasonable. However, if a guild said: "You must pay 100G every week or you get kicked out," I might leave that guild. That just seems shady, especially if it's not clear what the gold would be used for.
Otherwise you should be free to donate what you feel comfortable with. :)
I hope that if the guild is asking for money from lower level players like yourself, that they are making it up to you by helping you level, allowing you access to useful items in the guild bank, or having your repairs funded through the guilds coffers. If not, then be careful because once you deposit money into the guild bank, the guildmaster has full access to it and can sell all the items at the AH, clean out the funds from the banks and kick you out of the guild and there is nothing that you can do about it.
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