If you are serious about finding out some things, I suggest purchasing some equipment. None of it is very pricey, so don't worry about that aspect.
An EMF detector is good for detecting electromagnetic radiation.
In the paranormal world, they can be used to detect "spirits"... "ghosts"..etc.. if you were to get a high reading in an area you suspect to be
They can also detect high amounts of radiation, which can sometimes make people see things that are not really there.
Pretty cheap to buy.. I suggest searching for some on google to get an idea.
^The wiki for a typical EMF detector.
You can also use a recording device and attempt to get an EVP (electronic voice phenomenon.)
Audio recorders are also quite cheap, and can be very interesting.
Once again, google search EVP and you'll find some sites about how it all works.
Also, I suggest taking as many pictures around your house as you can... look for anything out of the ordinary in the pictures.
Dust and light reflections can appear to be "orbs" -- which people believe to be ghosts at times.
But you might see something unexpected.
In the end, there's no surefire way to find out if your house is haunted.
But, if things don't feel right to you and you still don't have "evidence" of the haunting, don't be discouraged. It's harder to prove than
(Once again, google searching for equipment or ideas on how to find things out will prove to be helpful.
Wikipedia may help as well.)