How does taxes work when buying we options using td ameritrade or tiger brokers?

Tiger broker user here. Only taxes there is is the 30% withholding tax on dividends. When you sell your stocks, there’s no tax. Only commissions.

If you're referring to capital gain/losses from option trading, there are no tax implications if you are an SG tax resident because those tax laws apply to US tax residents. Once you've filled out the W-8 Ben form, these laws don't apply to you.

The main tax law that SG investors should be wary of when investing in the US is the 30% withholding tax rate levied on the gross dividends paid out by US stocks.