300 Watt power supply, You must be using integrated video at the moment then? In any case, if you're going to put in a dedicated video card you will definitely want to upgrade the power supply to at least 500 watts (at least up into the GeForce 8 series, for 9 and above I am not sure, but I think the watt requirements are higher). 500 watt power supply will probably go for around $50. You will have to look around though, different places charge more or less.
To change it out, just simply remove the old one, disconnect all the connectors from the motherboard/other hardware and put in the new one; reconnect the connectors where the old one was. Just watch out for the 4 pin connector that hooks into your motherboard near the CPU (if the old one had it), you will need this or the CPU won't get power. Just keep a careful eye out and make notes of where the old connections are before you unplug them