mystery plant

A neighbor of mine gave me this plant and I have no idea what it is, it is very wet soil and I thought maybe it would be a good idea to replant it in drier soil. Can someone tell me what this is and how to take care of it.

Dieffenbachia.
There are many with different leaf patterns.
Yes, they appreciate a deep soaking then go quite dry between watering. Surprisingly dry for so tropical looking a plant. I have seen the planted in 3/8" lava rock for excellent drainage.

I have two leaves that are drooping down and I don't know why, there is enough moisture in the soil and it is getting plenty of light. So can anyone tell me whether to cut off the droopy leaves or leave it alone.

I think you nailed it when you thought the soil was too wet. It looks like your soil is very wet and heavy with little perlite or other material that would help get some oxygen to the roots. I would take it out of that pot, rinse off the roots and remove any parts that might be rotted and re-plant in a quality potting mix, avoid the brand X stuff. Water lightly until you see new growth then give it that good soaking and let it go dry in between waterings.

Should I just mist the soil or give it a cup of water? I have it on a styrofoam plate and I want to do it right.

As suggested above, transplant it, and remove as much of the existing soil as you can.
Repot into a much better draining soil. If the soil is damp when you are repotting it, then you soak it once to settle it into place that is all the water the plant will need for quite a while.

Simple trick: Lift the pot when you have just watered. Feel how heavy it is.
Lift it daily and feel how it is getting lighter. Dig a finger into the soil. The back of your finger, right above the finger nail is usually quite sensitive to temperature. Cool = wet. No real temperature feeling = dry.
Water it when your finger says it is dry, and get used to how light the pot feels when it is dry. Then you do not have to be digging holes in the soil to test the moisture.

Cheap moisture meter:
Freshly sharpened pencil.
When you poke it into the soil and the wood comes out dark it is wet.
If the wood comes out without a change in color, it is dry, so water.
If the wood comes out sort of blotchy, some wet spots, some dry, do not water.

I repotted it and set in front of the picture window, there is a curtain between it and the sun and I thnk it likes it there, one of the leaves that was drooping is notw perking up! Here is the pic.

Sounds good!

Good growing!

Yes, it is a dumbcane plant, I repotted it and gave it a drainage hole, I have it on the bookcase directly under the flourescent lamp and I think it likes it, as you can see it is growing a new leaf and the other leaves look good too. Here is a picture and I think you can tell, I probably should keep it there.

Glad we were able to help out! It is well on its way, now :-)

will post a update picture later, thanks again for the help:)

I am intending to leave the dumbcane plant where it is, it certainly likes it there. Here is another leaf opening up.

Thank you for posting back with follow ups.
Nice to see a success story!