The processor can only drop into the socket one way. I think there is a dot on a corner of processor that matches the corner of the socket with one less pin. Make sure the ZIF socket release lever is in up position before inserting or removing the processor from the socket.
It's the heatsink you have to pay attention to. Socket 370 has the raised portion on one side. The heatsink must not seat down on that. If it does, it will not make proper contact with the processor die. You can check the orientation of the mainboard/socket/processor and heatsink before putting it into the case. You might want to go ahead and assemble these before putting the mainboard in the case. I do. Heatsink/fans for the 370 are not large, heavy or bulky compared to later solutions.
The heatsink: If the heatsink has a TIM pad, leave the protective pulltab covering on until you are really going finally seat the heatsink onto the processor. If there is no TIM pad on the heatsink, follow the instructions for application of thermal grease by its manufacturer.
You know you have it right if the processor literally falls into the socket. Then check to make sure the heatsink isn't sitting up on the raised portion of the socket.
All standard, sane procedures apply.