Here are some tips to not only have a good time, but be safe as well:
1) PLAN your trip. Don't just go somewhere on short notice; You will wind up being seriously bummed out, or end up getting in some sort of trouble and regretting not being prepared.
2) Don't bring along a skeptic. I have done this and trust me, they just ruin the trip by trying to find an explanation for everything. Only bring along true abandoners.
3) As I saw on someone else's website: DO NOT park directly in front of the place you are exploring. If an area is indeed patrolled, you will get busted. Plus, you are letting others know that there is something of interest back there. The more people that know about the place, the less "abandoned" it becomes. Park a quarter mile down the road....get some exercise.
4) DON'T BE DUMB. If you see that a floor is rotten, do not attempt to walk on it. Do not go alone. USE YOUR HEAD.
5) Avoid other people, if possible. You don't know who they are, and maybe you don't want to. Not all people are sinister, but you never know these days. Also, the more people, the less creepy, and the less "abandoned" your trip will be.
6) If possible, go at night. Not only does this make it scarier, but it also sets the mood. Not knowing what lies in the dark woods just off to your right is much creepier than seeing that it is just a grove of trees (Or is it just a grove of trees?).
7) Be Respectful. Don't vandalize...leave the place cleaner than you found it....Let it there for others to enjoy.
8) Take pictures, make videos....have something to show what you saw, and share it with other "abandoners".