Here’s Abraham Hicks explaining what it feels like to connect to a departed loved one’s spirit.  Note – you usually you need to meditate first and be in a positive frame of mind (not depressed or grieving):

‘It will seem odd at first. You will think you are making it up. But you won’t be.  Notice the emotion that is present within you.  Did you feel the surge of vibration…a ripple…that’s your body interpreting their presence. You have the ability to interpret that vibration into meaningful conversation…they can offer you what they know, their awareness of you, what non physical is about.. You will get so that you not only feel their presence and hear them, but sometimes you will see them.  You will catch glimpses most often out of your peripheral vision because your peripheral vision is focused differently.  it will feel like someone was there and when you look they are not.  But they are there. Your relationship is just beginning.