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
MacBook "Core 2 Duo" 2.26 13-Inch (White Polycarbonate "Unibody" - Late 2009) (model identifier MacBook6,1) - this requires OS X version 10.6.1 build 10A2047 (note that this is a special build, "normal" 10.6.1 will not work; although I think 10.6.2 or later will)
MacBook Pro "Core 2 Duo" 2.26 13" (SD/Firewire 800 - Mid-2009) (model identifier MacBookPro5,5) - this model requires OS X 10.5.7 build 9J3050 (again, a special build; I don't remember if "normal" 10.5.8 will work, but I'm pretty sure 10.6.0 would)
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.