First, the supplies:
sandpaper - both fine grit and rough
paintbrush an appropriate size for the surface to be covered
Sand any obvious rough spots with the rougher sandpaper. Be sure to check for dents in the wood as well. Edges should be lightly sanded to take off any splintering that may have happened in the building or cutting process. Use the tack cloth to remove any sawdust. This is a must for working with wood. This cloth, available at most hardware stores, will remove grit that regular cloths or rubbing with hands cannot. Finish the sanding by going gently over the piece with the fine sandpaper and then again with the tack cloth.
Now, you are ready to prime! Depending on what your final product will look like will depend on which primer you choose. Gesso has more tooth (i.e.: it is rougher) than plain white acrylic paint does. If you are hoping for a smoother finish, the acrylic paint may be the better choice. If the final product will be very dark in color, it may be best to choose a medium gray paint. Any of these choices will seal the wood. Some wood, pine in particular, is very difficult to seal with only one coat. You may need two. Be sure to dry each coat thoroughly.
Once the wood is primed, you are ready to begin your project! Depending on whether your project will end up outside in the weather or inside will decide whether you need to weatherproof it. Mod Podge is a good choice for painted rocks and other things. It will not last forever, but it will protect items both inside and outside the house. Varnish or shellac will do a better job of protecting items that are meant to be permanently outside. Much depends on your climate, whether the item will be in direct sun, etc.
As always, enjoy the process and have fun!