how do i connect my imac to hp deskjet1512 printer

Unfortunately that printer has manufacturer drivers only for 10.6 and later.

If you have a G3, G4, or G5 processor, you may only be able to use some open source drivers listed here

with that printer*:

http://www.macmaps.com/printersx.html

Otherwise, upgrading to 10.6.8 is highly recommended using this tip:

https://discussions.apple.com/docs/DOC-2455

Once you've done that, here are the drivers:

HP Deskjet 1510 All-in-One Printer series Full Feature Software and Drivers - Mac OS X v10.6, v10.7, v10.8, v10.9