There's no 'quickest' way to travel by train from Bangkok to Kuala Lumpur.
Firstly, you have to get the BKK-Hatyai bound train at Hua Lumpong station (which runs daily) at about 3pm. Ticket costs about 800Bt.
Arrival time at Hatyai Junction should be about 10am to noon, where you'll have some time to do shopping, short nap, bath, etc. However, do remember to get the next ticket to Kuala Lumpur RIGHT AWAY (before its sold out). Train leaves at about 4pm and ticket costs about 800Bt. (approximately, and I can't remember... its about that the last time I took it and Hatyai-KUL costs more than KUL-Hatyai).
You'll have to do your immigration checks at Padang Besar station, which is about 1-2 hours away from Hatyai Junction. From there onwards, you're on your way to Kuala Lumpur. You'll arrive KUL at about 8am in the morning.
Hope this helps and good luck!
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