How do I opperate osx 10.4 from a USB stick on a Intel Core 2 Duo 2.26 GHz 2GB laptop that using OSX 10.7.5?
As I'm having problems with non compatible Power PC programs that I need to use.
Short answer: you can't. But you may be able to use 10.6 and/or 10.5 instead.
Longer answer: I can't tell from your description exactly which model you have. It could be either of two models, neither of which can run OS X 10.4
In either case, you can run a suitable version of 10.6 and/or 10.5; neither can run PowerPC program natively, but both had Rosetta available to translate them for the Intel CPU. Rosetta was standard in 10.5, and an option (installable at any time) in 10.6. It is not available for 10.7 or 10.8.
To install an older version of OS X on a USB drive, you'll need a suitable installer disc (either the one that came with the computer, or a generic installer with a later version that had support for that model rolled in). Format the USB drive in Mac OS Extended (Journaled) format, with a GPT partition table, then boot from the install DVD and install onto the USB drive.