I'll be talking about public transport in Kuala Lumpur because that is most probably the first place in Malaysia you'd explore. Public transport in KL is fine, in particular, rail transport.. it's not as integrated as the rail systems in Hong Kong and Singapore wherein interchanging from one line to another is a breeze. In KL, there are some stations with the same name (from different lines) but are usually some distance apart from each other. When interchanging, you'd have to get out of one station and get in on another. As for prices, they're way cheaper than Hong Kong or Singapore's rail systems. Generally it's safe.
To get to KL Sentral (the central rail station in Kuala Lumpur), I suggest you just ride the KLIA Ekspres. It's a non-stop high speed train that will take you to KL Sentral in 28 minutes. 35 Malaysian Ringgits (MYR) one way (cheaper and faster than taking the taxi; usually it will cost you 70-80 MYR and it could take more than an hour).