Bangkok is a hub for many destinations in South-East Asia and, as a result, there are a large number of airlines flying directly to Bangkok from Europe, USA, Australia and Asia. If you plan to travel around the Christmas and New Year period book well in advance since this can be a busy time of year.
Trains run between Singapore and Bangkok, with stops along the way in Malaysia, before entering Thailand at Padang Besar. You can choose first or second class sleeper accommodation, or third class (seat only). The trains are quite comfortable and are a good way to travel if you are on a budget.
Buses and taxis enter Thailand from Malaysia at Padang Besar.