First, warm up for about 20 minutesget really sweaty. Then start with some exercises that work your core, like crunches, medicine-ball twists, and good mornings (when you take a body bar on your shoulders and bend at the waist down to 90 degrees and back upbut make sure to stretch your hamstrings first). Do these three days a week in just one set of eight to ten reps. Since you're new to them, it won't take much for your muscles to react.
Work on some basic upper-body strengthening through pushing and pulling movements like knee-down pushups or bench pressing; lat pull-downs, assisted wide-grip pull-ups, and seated cable pulls; tricep extensions and standing barbell curls (done with your abs engaged).
Make sure to use enough weight that the last two reps are challenging, and work with a spotter on the bench presses. Focus on good form, and let the weights down slowly. In the last half of your training period, start using dumbbellsthis will challenge new stabilizing muscles on the periphery of your lifts and prepare you for the independent movements your arms will face on the water.
Alsoand this is importanttake up some sport-specific drills. Kayaking is about rotational movements generated from the core, and pushing with the opposite arm more than pulling, so you'll need to mimic these movements in the gym. Start with little-to-no weight, and switch to cables after some practice. Consider doing a rotational one-handed cable cross, or a "wood chop," where you pull the cable down from the opposite upper corner toward your outside knee, as if swinging an ax.
In all rotational movements, keep the weight low in the beginning, bend at the hip, not mid-back, and engage your abs throughout to hold your form and protect your lower back. Be sure to ease off on the weights the week before you go, so you don't show up exhausted. Have a great trip!
For more strength training tips, check out Paul Scott's National Magazine Award-winning article series, "The Shape of Your Life."