I treated my collected driftwood by boiling in a pot of water for 1/2 hr. That is mostly to get water into the wood so it will sink. For porous stuff like wood, you want the heat to get into all the crevices, and it takes a bit of time. <To really sterilize things, you'd need a pressure cooker for maybe 10 min or so, but 1/2 - 1 hr in boiling water should be pretty good.> For solid surfaces, you only need to have to surfaces hot (there shouldn't be anything nasty growing inside solid material), so you can reduce the time of contact. 5 - 10 minutes in boiling water should suffice.
I bleach solid surfaces because it is less work. <You might not want to bleach porous stuff like wood as it would be difficult to be sure of getting out all the bleach after.> A 1:10 dilution of household chlorine bleach should do the trick. I wash & soak in bleach for 5 min or so, then rinse, rinse, & rinse some more. <I use the garden hose on the lawn & go to town.> After you rinse enough that no smell of chlorine remains, soak in water with a double or triple dose of dechlorinator. The material should be safe to use at this point. However, I go the extra step of air drying & sun baking for a few days just to be sure all traces of bleach is gone.
If you are wary of using chlorine bleach, you can use oxygen bleach (ie H2O2). Peroxide gets expensive so I use that for small stuff. I use a 50:50 mix (you can also do full strength). Soak for a few min or until all foaming or bubbling stops, then rinse. Since H2O2 breaks down into water in light, all you have to do is let the stuff sit out in the sun for a day or so & it will be safe to use.