Think of the exchange rate as the price of a currency—in this case the Thai baht. So the exchange rate (THBUSD in this case) is just how many USD you need to buy one THB.
As you said, multiple factors determine the equilibrium price of the currency... most often quoted is perhaps the continued current account surplus (more or less that Thailand exports more than it imports). When a country exports, foreigners need the local currency (THB) to buy Thai goods. This drives up the demand for THB and hence its price.
Influencing the price
Can the Bank of Thailand set the price of THB? Yes, in a sense. Just like anyone could set the price of a banana. This is called FX intervention.
Let's say you think the price of a banana (right now \$5) should be higher... at \$10. What you need to do is to drive up demand. You go out and say you're willing to pay anyone \$10 for a banana. Naturally, nobody would be selling bananas at \$5 anymore because they know they can sell one to you for \$10.
Problem: you could quickly run out of money. This was basically what happened in the Asian Financial Crisis of 1997. When you can't buy bananas at that (artificially) high price anymore, you say, sorry guys... no more bananas for \$10. The price of bananas fall.
John's paraphrase: Let's say some banana seller thinks he doesn't earn enough with the current banana price (right now \$5) and decides to lift the price (say \$10). By humanity's most common economic model, most rivals will start to sell it in the same price. Banana buyers will lose money and will keep losing it until a protest that would bring the original price back.
A: This is not entirely correct. What the central bank does in this case is to act as a buyer, buying up any bananas available at the price of \$10. This creates an infinite demand for bananas at \$10, driving up the price. This is the green line in the chart (please excuse my poor drawing.)
Now let's say you think the price of a banana should be lower (to help exporters, for example)... at \$1. What you need to do is simply to increase supply. Concretely, you start growing bananas like crazy and announce that you'd sell all bananas you have at \$1. Naturally, people will buy from you instead of from other sellers.
Problems: If people believe bananas' equilibrium price is actually \$5 and not \$1, then all of the sudden bananas become very attractive as you can buy them for very cheap. They'll want to buy more, driving up the price.
In addition, you're now full of cash (USD). People say, this guy has lots of money (foreign exchange reserve) so if there's negative shock to bananas (people start to realize that bananas are bad for your health, which would have driven the price of bananas lower, to \$0.5, for example) he could still manipulate the market so that the price remains stable close to \$1.
Knowing this, poeple see bananas as a safe asset and demand even more in times of uncertainty, driving the price of bananas even higher, going against your intervention. One more problem is that some country labels other countries "banana price manipulator" if you sell too much bananas ;)
John's paraphrase: By the model, a seller who wishes to lower his price, should increase supply. He could grow bananas and sell them in \$1 and usually people will buy from him instead from his rivals. If people assume bananas are bad for health they would buy less and that seller will sell in \$0.5 Some rivals might gang up to affect the masses not to buy from him.
A: The first part is correct. The part after, "If people assume bananas are bad...," however, is not. I've updated my answer above.