Surfing is NOT easy to pick up. I started surfing in the 6th grade, and I've spent a lot of time with other surfers. No one begins to get even to a competent level in a week. Surfing requires strong arms (you're constantly using them to paddle yourself into waves... back out to the peak, adjust position, etc), and good balance. You don't need exceptionally strong legs or stomach muscles, but it certainly wouldn't hurt to have them.
If you don't do a lot of endurance type excercise with your arms (like swimming or rowing) they're going to tire out really quickly. You'll be sore after 45 minutes.
To really get the hang of surfing, you have to stick with it and go do it a couple times a week for several months. After 4-6 months, you can get to the point where you really start to know the basics and can develop your technique.
Don't worry about sharks or injuries though. In a decade of surfing, my most serious injury required seven stitches (I got hit in the head with the fin on my board). Other than that, I never had any injuries I would consider serious in the least, just small cuts and bruises.
Learning to surf is not like most other sports. When you're learning to snowboard and you fall, you just stand up and try it again. When you're learning to surf and you fall, you have to paddle back out to the peak before you can try it again. Also, on your way out to the peak, there are waves coming in that you have to contend with. When you're paddling skills aren't very good, it's really easy for each wave that hits you to push you back towards the beach farther than you're able to paddle back out before the next wave.
Start on small waves, and go with someone experienced who can give you tips on how to paddle and where to sit in the water. The thing about teaching someone to surf is that you really don't teach them how to stand or surf or do tricks on the board. You teach them how to paddle and where to sit, because the hardest part is catching the waves. Once you've caught the wave, then standing and turning is something you'll really have to figure out mostly for yourself.