If we are talking about a fixed exchange rate , the currency (let's just say AUD, even though it is floating) will be undervalued if demand exceeds supply - thus the central bank must sell AUD (i.e. buy foreign currency) to keep it at this level which will increase the level of foreign reserves.
If the currency is overvalued, the supply of AUD exceeds the demand of AUD, thus the central bank needs to buy AUD (i.e. sell foreign currency) to keep it at this level, reducing its level of foreign currency reserves. Eventually, these foreign currency reserves will run out (e.g. Asian Financial Crisis), forcing a devaluation of the currency or a float (generally before it gets to this extreme stage).
If the currency is floating, it's not really over or undervalued - these terms generally refer to market equillibrium price compared to actual price. However, one can consider the currency over or undervalued in terms of how much it is worth taking into account the fundamentals of the economy, although the RBA intervention, I believe, is generally to smooth out fluctations.
With the floating rate, the central bank can enter the forex market as a buyer or seller (termed 'offical intervention in the forex market) to influence the exchange rate as laid out above, either directly or getting another central bank to act on its behalf.
the government can use foreign reserves to buy $, therefore reducing supply of $ and driving the exchange rate for $ up
This is WRONG, and you will lose marks for writing this in the HSC - the governmen entering the market increases the demand, rather than reducing the supply. What he means is that they buy up the extra supply, but you will lose marks for that.
The RBA also influences the exchange rate through the sale of 2nd hand gov't securities, as grimreaper said. With a higher exchange rate, there is increased investment in interest bearing assets in Australia (read bonds), causing increased demand for the currency, and reduced capital outflow.
Lastly, the RBA can try to turn around market sentiment by the release of some offical annoucement talking up the currency. This is the most simple to understand of the three processes - basically the RBA advertises the dollar in the hope of changing perceptions. This is commonly refered to as 'jawboning'.