The reason people don't talk about seeing ghosts in Christian circles is because people are afraid of the sorts of responses that they will get. Some Christian circles seem to believe that anything on the topic is automatically occultic. Its ridiculous too, when you consider that even Christ showed himself as an angel/ghost before he showed himself as fully risen. Certainly the women saw some sort of spirit! In Matthew 14:22-33, Mark 6:45-52, John 6:16-21 his followers thought Jesus was a ghost when they first saw him walking towards the disciples' boat on the water. They clearly felt this was a reasonable description of what they saw until Jesus spoke to them. The apostles were okay with wondering if they had seen a ghost. I think we are still allowed to wonder too.
The Bible mentions people as alive after death ~ in Mark 12: 24-27 Jesus specifically says that Abraham and other servants of God still are alive in some sense ~ but usually not still on Earth at the same time. The Bible mentions angels & demons - as beings who were never human, but could affect us here on Earth. Prophet Daniel saw visions of glowing servants of God too.
But does the Bible specifically affirm anyone seeing a ghost? Well ~ in 1Samuel 28:5-9 the OT says that the Witch of Endor sought the spirit of the Prophet Samuel for King Saul (and was rather afraid of him when he suddenly arrived!) This wasn't a happy visit. Samuel informed Saul that he was about to lose his life and had already lost God's favor. Saul's kingdom would be given to David. I am pretty sure this isn't the message the woman would like to have obtained. Some Christians think this was a demon pretending to be Samuel, but if so, it was strangely faithful copy.
(The Bible is absolutely against people seeking to call up or channel spirits, seek omens or engage in other forms of witchcraft Deuteronomy 18:9-14 - but that doesn't mean God didn't send Samuel one more time to rebuke Saul, hopefully into repentance...)
Jesus' parables include the afterlife situations of a beggar named Lazarus and a wealthy man who knew the beggar in life. The rich man begs that someone go back (as a ghost presumably) to warn his siblings against his fate::
 "He answered, 'Then I beg you, father, send Lazarus to my father's house,  for I have five brothers. Let him warn them, so that they will not also come to this place of torment.'
 "Abraham replied, 'They have Moses and the Prophets; let them listen to them.'
 " 'No, father Abraham,' he said, 'but if someone from the dead goes to them, they will repent.'
 "He said to him, 'If they do not listen to Moses and the Prophets, they will not be convinced even if someone rises from the dead.' " Luke 16: 27-31
I'd say this is the reason we Christians don't usually expect to see ghosts. We know God rules all parts of creation - including the portion we consider the 'afterlife' (according to Revelation 1:18, Jesus owns the keys from death & hell), and God is against our living in fear. Not many of us would feel anything else if we could be haunted at will by those who have passed over. Additionally, it seems Abraham, at least, didn't see much point in "Christmas Carol"-style visitations..at least in this case. Abraham doesn't say 'no one is ever allowed to come back' - he says that these rich people would not repent if Lazarus did return. There is a difference.
However you look at it, the Bible is pretty clear that there are spirits in our material world...starting with us.
It is important to remember that we are multi-dimensional (spirit, body, soul) and so are angels. Unless what someone sees inspires fear or suggests things that are anti-God, I wouldn't worry excessively if a friend or family member said they saw something 'ghostly.' Some people have been given that gift.
One thing we do here, when spirits are sensed, is to pray that only that which God allows to remain. Prayed sincerely, this will release our guardian angels to deal with any enemy action.
I believe there are 4 ways to sense "spirits"
1) You may have encountered a physical recording of a past event.
Certain combinations of say, mineral-rich sheet rock and celluloid-rich earth can "record" (like a VHS or cassette tape). These 'playback' under high energy conditions, like lightening storms. Several places have been proven to be repeating old events in this way.
According to one documentary my family saw, there's a medieval tavern in Britain that replays an evening from long ago (complete with singing, clinking mugs, and laughter) in every strong storm.The sounds are recordable. It never changes. The walls in the place have an unusual mineral composition that may well be responsible. Its weird, but not necessarily any more demonic than a hidden tape recording from your childhood.
If a field 'recorded' a man walking over it, and it plays back inside the house now built on it, you will see him 'swim' through the floor. (My family actually saw this.)
How do you tell?
Its always the EXACTLY same event...voices ..shapes. They do not change. They do not react any more than a movie would.
2) Angels...usually only seen when you need comforting or a message from God.
Fallen angels- called demons- will pretend to be 'good angels,' 'aliens,' powerful versions of themselves, or 'ghosts' of people, and given that they have also been around a long time, they can lie very effectively!
Pray hard about any 'visitation' that seems very scary...or very wordy...
3) The classic ghost...someone who is (still) around without their body. They can't hurt you. They don't usually speak. Many times these are friends and family who may have asked to see you before leaving the Earth. Many believe that God sometimes grants given permission for a spouse or parent to watch over a loved one after they pass on. These may include pets.
I know that one great-aunt believed her husband was still around. I can't answer this for certain, as I never saw him, but whenever a storm or bad person came by, you'd hear a whistle and all the doors and windows would slam shut one by one. Sometimes they'd slam right in front of us, so we asked 'the ghost' to shut the ones we weren't near for greater efficiency (it also cut down on the heart palpitations!). Our request was granted at the next storm. Yes, they were Christians.
People claim there are "confused" ghosts, still hanging around... I can't speak to this, since two other categories could account for most of those 'sightings.'
I do classify 'live' hauntings here. My husband, especially, is extremely prone to this.
My husband's health has been precarious all his life. He also used to smoke, as his mother smoked carrying him and he grew up with it. Nevertheless, he had always been somewhat allergic to it, and, even worse, the swelling and damage in his gut cavity sometimes limited his diaphragm. He had coughing spells that were scary to behold.
Sometimes when he had a bad spell away from me, he would appear on the stairs or in the downstairs bathroom, coughing away... :(
He 'died' briefly in a medical procedure in the early 90's. I (and a room full of waiting patients & their families) watched him walk out the door as a spirit and disappear (meantime we could all hear them yelling CODE BLUE) in the other room. He appeared at home and was seen by our infant son (who chortled with glee to see him and asked to be picked up), my Mom, and our daughter. (He appeared at the doorway, but didn't walk back through the room when he woke up. Don't know why.)
Tom's brother hung around for weeks after he passed on. We all saw him. We know why he was there. He hadn't visited with us much in life and was trying to be friendly. My kids were playing Wii Fit one evening, and he appeared next to them trying to model the right stance and moves to win the boxing challenge. He vanished when they got it right.
4) 'After image'...Sometimes we get a 'ghost effect' from cued memories.
If you look at a bright object and then look away, you can close your eyes and often see a purple reflection. The ghost effect seems to work on a similar principle. Either we got too strong an imprinting on an event or person to lose it right away or something happened so often that our brain adds back to the scene something very expected.
We may 'see' a chair where it always used to be, or 'hear' a person who always greeted us on the way to work. If the chair often held a loved one or the person who greeted us has passed over, we may think this is a ghost, instead of a 'mental echo.'
Some believe that the imprinting is actually on the scene...that the wall records spiritual residue of big events that happened nearby, or the chair in the example above still has some energy from the person who always used it. I can't answer to this, and I think it would be hard to prove. It seems to me that even if this belief is true, it would be another 'recording' - physical in a way we can't yet measure. I doubt that such phenomena would violate any spiritual principles one way or the other.
I do know that on land where much sincere praise or praying has occurred the earth feels peaceful, joyful,many years later - as though the rocks, grass, dirt, plants etc are still reverberating the echoed praises to Almighty God. Maybe the angels are still singing along.
Its good to know that whatever we 'sense,' God is in control.