You can drive into Singapore via the Causeway and the Second Link. Okay, that sounds simple on paper, but in fact it is rather complicated and expensive, particularly if you are not driving a Singapore-registered vehicle.
For Malaysia-registered cars
You need to show that your car has a valid road tax and Malaysian insurance coverage. After you go through immigration and got your passport stamped, proceed to get a vehicle entry permit called an Autopass Card, available at the LTA (Land Transport Authority) office at the Woodlands and Tuas Checkpoint arrival zones. To get the Autopass Card, fill up the application form (here's the link for the online copy) and pay for the Autopass Card which costs S$10. The officer from the LTA will inspect your parked car, verify your road tax and insurance cover note, and then issue you a chit to pay at the LTA Counter for your Autopass and rental of the In-Vehicle Unit (IU) for road pricing charges.
The Autopass Card is issued to your vehicle. It is non-transferable between vehicles. If you want to bring a different car into Singapore, you will need another Autopass Card. You have to top-up the Autopass Card with sufficient cash value to pay for your VEP fees, toll charges (where applicable) and ERP fees (if applicable). An alternative to pay-as-you-drive is to opt for a flat road pricing fee of S$5 per day.
The IU is mounted on your dashboard and the Autopass Card inserted into the card reader of the installed IU. The IU will record the entry and exit of your car into Singapore, and display the amount of VEP, road pricing charges and tolls you incur.
Next, you proceed to drive your car to Customs, where you open your boot for inspection. Once you are okayed, you are free to drive anywhere in Singapore.
You are allowed ten days of driving in Singapore for each calendar year without paying the Vehicle Entry Permit (VEP) fee. If you are going to drive more than 10 days in Singapore, you will have to pay a VEP fee of S$20 per day.
When you are ready to leave Singapore, you pay by slotting your Autopass card to the card reader at the immigration counter where you get your passport stamped.
For non-Malaysian foreign-registered cars
Everything mentioned above applies except that instad of the Malaysian road tax and insurance coverage, you need a Vehicle Registration Certificate, Customs Document (Carnet), Vehicle Insurance purchased from a Singapore-based insurance company, and International Circulation Permit.
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