Not like you would think. To you and I they would feel sticky and their tentacles will stick to your skin. A fish is much smaller and therefore can be hurt and/or killed by one. The only anemone that I know of that we typically keep in our aquariums that can actually attack a human is a large carpet anemone. Even then, it would be merely very itchy where it touched you and maybe cause that area or your body to swell that it came in contact with. A friend of mine had a very large one attack his forearm while he was moving it from one tank to another, but that anemone was aobut 15 inches across. So unless you are very prone to being allergic or maybe already have some serious known allergies to bees or something similar, then I am going to say you should be fine.
You should seriously wait until your tank is at least 6 months old before adding one though. They are very delicate and have specific requirements of lighting and water quality that is important to maintain. Newer tanks tend to have serious fluctuations and it has a good chance of dying if introduced too quickly. Do you have a specific one that you have in mind?