The most important power connections to get right are those between the motherboard and PSU. There are usually two; refer to your motherboard manual for their locations. On the ASUS P5E-VM DO pictured there are two, the ones most consistently used for a modern desktop PC (those required by the ATX12V2.2 standard). They are the 24-pin connector (in the yellow rectangle) and the 4-pin ATX 12V connector (in red).
Your PSU will only have one 24-pin connector (or a 20+4-pin, which can be used with older motherboards that use 20 pin connectors or the newer ones). In all likelihood it will only have one 4-pin connector as well, though it might have an 8-pin or 4+4 pin also, again allowing it to work with older motherboards.
Simply make the appropriate connections as shown below. The connectors only go in one way, but they can take a bit of shoving. Make sure they are oriented correctly before you lean on them. The little tabs will catch, as shown in the pictures of the 4-pin connections.