Installing coil overs in a 2003 Honda civic?

Yes they fit over your stock strut. if you didnt buy a complete kit.

just jack your car up..unbolt your current set up (engine bay and in the trunk area usually)

take off the old springs.(but be careful cuz there compressed. i think you need a special tool)

intall the coilovers onto the struts..and you need a special too for this too

then put your suspension back together

be carefull not to break your struts.

if by coil overs you mean thoes things you can get on ebay for super cheep just sell them and save up for quality coilover and shocks. your ride quality is going to suck with stock struts and these coil overs or pretty much any lowering spring. dont cheep out when it comes to your car if you care about it.