There are two land routes from KL to Singapore - one is through the Johor Bahru (JB) town where you drive across the Causeway (that's the bridge) into Singapore. The other is through the Tuas 2nd Link (newer, smoother and less traffic), for which you have to exit the highway (look out for signs saying Tuas 2nd Link, or the Senai airport exit) before reaching JB town.

There are highway tolls along the way from KL to JB, so be prepared with cash to pay (can't remember exact figures but total should be less than RM100 or US$25).

The Tuas 2nd Link route is slightly more expensive (toll) and hence has less traffic and/or passengers at the immigration checkpoints.

Passengers in cars do not need to offload belongings and walk across the immigration/customs - you hand in your passports at drive-pass booths. If necessary, the customs will stop you for a quick check of your luggage at other point as you drive pass.

There are however complications when driving in Singapore on weekdays - namely the tolls (ERP) Singapore charges on some of their roads and highways which use specific in-car devices. Cars coming in from Malaysia need to install such devices (with a cashcard) at some point after immigration.

Singapore also charges Malaysian cars SGD30 per car per day on weekdays. Weekends (Friday after 7pm - Sunday) are free.

Oh I just found a link with all the details:

http://www.visitsingapore.com/sections/articles/4a/0,1176,760,00.html

Hope that helped!