When travelling in central Bangkok, I would recommend using the Skytrain (BTS) whenever possible, as it is fairly cheap, and is convenient and air-conditioned. You usually wouldn't have to wait for more than five minutes for your train to arrive.

Soon the subway system will be opened (not sure of the date), which should be a big improvement for the city.

Besides the BTS, there are Taxis that are also quite cheap - around 35B for the first 2 kilometers, then it slowly increases. You may find some 'illegal' taxi drivers that will try to bargain a price for you. eg. They will say 'Where u going?" Then would give you a price usually over 100B for a 40-50B trip. So make sure you get them to use a meter unless you are sure about the cost of the 'bargain'.

At first I tried tuk-tuks a few times, (3 wheeled vehicles) but because you need to bargain a price with them I found most drivers very dishonest, and some even ask you to go to a 'jewellery store' or a 'temple' and they will discount your price. Once a driver asked me to look in a jem store to reduce our price (he would get a petrol coupon from the owner of the shop) - but because I didn't buy anything from the store, he couldn't get a coupon, so he couldn't offer me a cheap price. I would now usually walk than get a tuk tuk.

Most of the times I found that a taxi would get me to a place cheaper than the price most tuk tuk's ask of foreigners, but if you are desperate for a quick trip in a tuk tuk, make sure they don't charge you too much, i.e. for most places within Bangkok it shouldn't be more than 50B.

There are also many motorcyle drivers that offer people rides for a bargained price, these prices may be fairer than a tuk tuk depending on the person, but it's also a bit more dangerous.