I agree with everything Mr V has said. You should be very careful before bunging any medicines in a tank (with the exception possibly of Melafix, since that's pretty well harmless as far as I can tell), and only treat if there are frank signs of infection.
Yes, you do need a hospital/quarantine tank.
I don't always use a quarantine tank myself because sometimes I've found the extra stress of moving the fish makes the situation worse. However, this is a risk and not necessarily to be recommended (OTOH, I do get my fish from an excellent LFS who I trust). I don't automatically use a hospital tank either, depending on the problem. Ick, for instance, I tend to treat the whole tank. But if one or two fish are unwell in specific ways (I have a fish with dropsy in there are the moment, for instance), I definitely use a hospital tank. My earliest hospital "tank" was actually an orange bucket with a sponge filter and a heater in it - it doesn't have to be a fancy set-up.
Methylene Blue is excellent for fungal infections and ick, and a useful aquatic disinfectant. However, it is toxic to filters and if you are not careful, you could crash you tank (i.e. cause it to have to cycle again). I wouldn't recommend it to a newbie. Stick to safer meds - I use the Interpet range. They are generally safe and are supplied with good instructions.
Your proper procedure should be to set up a quarantine tank, using matured filter media (keep the sponge filter in your main tank for a week before), water from your main tank and a couple of cheap plastic plants. Put your new fish into the tank in the usual way and observe them for about 10 days. You can put a little Melafix in there if they show signs of anything worrying. Another advantage is that you can treat with salt, without worrying about corys or snails or whatever.
If during the 10 days, the fish seem unwell, treat with the appropriate remedy. Ick and fungus are the most likely problems. Do not move to the main tank until they are well and truely cured. If the fish are fine after 10 days, more them to the main tank, but continue to observe them closely for a little while after that.