Take a bus, train, boat from Singapore to Johor Bahru Malaysia. There are many routes you can take, but travelling by road is the easiest.
The Singapore - Malaysia border checkpoint crossings with customs and immigration:
1. Changi Airport - airlines flying worldwide and from Singapore to Malaysia.
2. Selatar Airport - scheduled flights from Singapore to Tioman island (Malaysia) and Batam (Indonesia)
3. Causeway link from Woodlands checkpoint (Singapore) to Johor Bahru city, Johore (Malaysia), by road. A major crossing.
4. Second link at Tuas, Singapore - road links to the North-south (PLUS or toll) expressway in Johor, Malaysia - by road; most coaches to Malaysia travel this route.
5. Railways - from Woodlands, Singapore for Singapore immigration and at Tanjong Pagar (Singapore) for Malaysian Immigration (confusing?!); from JB railway station you can travel to KL, until Padang Besar and on Thai railways up to Bangkok.
6. Ferry terminals and checkpoints - from Singapore to JB: Changi Point Ferry Terminal (CPFT) at Lorong Bekukong and Tanah Merah terminal. minor crossing
7. Singapore Cruise Centre, Harbour Front Centre, at Maritime Square - for cruise ships going to Port Klang, Penang, Kuching or Langkawi.
Check details at mymalaysiabooks
