JOEL - I think that with today's media we have been conditioned to think that a posessed person is going to be thrashing around on a bed, spinning her head around, and spewing out pea soup. While there have been instances of posessed people doing strange things with their bodies, most people who are posessed of an evil spirit are going to look normal but perhaps be prone to do evil things or there will be a feeling of evil sensed by those around them.
Harold B. Lee related his expierence with evil spirits:

"I want to bear you my solemn witness that I know there are such forces in the world today. It would seem to me somewhat significant as I have thought about it, that the first and only experience of its kind I ever had, came shortly after I came into the Council of the Twelve when I was asked to administer to a young woman who was possessed of an evil spirit. Seemingly, there might have been a purpose in letting me know that these powers were around. In this experience, as I was challenged by the evil spirit, the hairs on my head felt as though pin pricks were in every hair and coursing down my body. I knew in that experience the power of evil, and I knew again the superior power of the priesthood and the powers of the Living God. (conf report 1949)

One who has let Satan influence him will be inclined to distance himself from God. Nephi said:

"for the evil spirit teacheth not a man to pray, but teacheth him that he must not pray." (2 Nephi 32:8)

We are told in the scriptures in regards to true prophets, "by their fruits ye shall know them" (Matt 7:16, 20). This could also be applied to those, who through sin or poor choices, have allowed their souls to be controled by an evil spirit. Satan does have the power to "bruise our heel" (Moses 4: 21) , and if we let him, completely take over our souls. One who has allowed himself into this condition will bring forth bad fruits and will try to bring others down with him.

The Apostle John has written these words,
"Beloved, believe not every spirit, but try the spirits whether they are of God.
Hereby know ye the Spirit of God: Every spirit that confesseth that Jesus Christ is come in the flesh is of God:
And every spirit that confesseth not that Jesus Christ is come in the flesh is not of God" (1 John 4:1-3)

Joseph Smith said of Satan's influence:

"A man must have the discerning of spirits before he can drag into daylight this hellish influence and unfold it unto the world in all its soul-destroying, diabolical, and horrid colors; for nothing is a greater injury to the children of men than to be under the influence of a false spirit when they think they have the Spirit of God."
He also spoke of the requirement to have the gift of revelation to be able to have this discerning of spirits. (Discourses of the Prophet Joseph Smith, p. 112)

President George Q. Cannon wrote:
"I will tell you a rule by which you may know the Spirit of God from the spirit of evil. The Spirit of God always produces joy and satisfaction of mind. When you have the Spirit you are happy; when you have another spirit you are not happy. The spirit of doubt is the spirit of the evil one; it produces uneasiness and other feelings that interfere with happiness and peace. . . .
When you awake in the morning and your spirits are disturbed, you may know there is some spirit or influence that is not right. You should never leave your bed chambers until you get that calm, serene and happy influence that flows from the presence of the Spirit of God and that is the fruit of that Spirit. So, during the day you are apt to get disturbed, angry and irritated about something. You should stop and not allow that influence to prevail or have place in your heart. (Mar. 23, 1873, JD 15:375-76)

So posession by an evil spirit is not always going to be manifest by uncontrolled body movements and mouth as depicted in the movies; more importantly it is identified by the things a person says and believes, and the absence of the holy spirit. We can discern these through the gift of revelation by staying close to God and His spirit.