I'll assume that your new card is hardware-compatible with your PC. (The most common problem would be having an inadequate power supply.)
The generic approach to putting in a new graphics card:
Have the drivers for the new card in hand. (CD that came with the card, or a fresh download. The download is probably more up-to-date.)
Uninstall the drivers for the old card.
If you can power down instead of restarting Windows, that would be preferred. If not, let Windows restart. If the old drivers were really uninstalled, you should get generic VGA drivers. Shut down the PC. Unplug it. (Or turn off the power supply switch, if it has one.)
Swap the cards, being careful about electrostatic discharges.
Power up the PC.
Install the new card's drivers.
Off you go...