How to buy and trade stocks worldwide?

I am currently using Interactive brokers. Cannot comment on other brokers.
For US stocks, for every 100 shares, you will be paying 30 US cents. This does not include the fees charged by the stock exchange such as clearing fees and etc. The total cost will definitely come in at less than one US dollar for every 100 shares.
There is a catch for using IB. If your holdings including cash are less than US 100K, they will charge you US$10 on a monthly basis.
http://investment-blueprint.com

You will need access to a broker that allows you to buy stocks from your desired market. Your example of Facebook and Tesla are listed in the US market so you will need a broker that can do this. Not sure if OCBC can do this but even then the transaction fees (comms) will be horrendous.

Cheapest examples will be using interactive brokers or Td Ameritrade. I use the latter and comm comes to 5 USD per stock transaction. As a comparison, the local brokers will charge at least 20+ per transaction.

Do note that your CDP account will only hold SGX stocks which are not held in a custodian account with your broker. Hope this helps