The church teaches and discourages having tattoos and body piercings. Pres Hinckley gave a memorable talk to the youth and young adults of the church back in Nov. 2000. It was reprinted in the Ensign Magazine in Jan. 2001. 
 
Here is an excerpt:  
 
"I promise you that the time will come, if you have tattoos, that you will regret your actions. They cannot be washed off. They are permanent. Only by an expensive and painful process can they be removed. If you are tattooed, then probably for the remainder of your life you will carry it with you. I believe the time will come when it will be an embarrassment to you. Avoid it. We, as your Brethren who love you, plead with you not to become so disrespectful of the body which the Lord has given you." 
 
"May I mention earrings and rings placed in other parts of the body. These are not manly. They are not attractive. You young men look better without them, and I believe you will feel better without them. As for the young women, you do not need to drape rings up and down your ears. One modest pair of earrings is sufficient." 
 
"I mention these things because again they concern your bodies." 
 
"How truly beautiful is a well-groomed young woman who is clean in body and mind. She is a daughter of God in whom her Eternal Father can take pride. How handsome is a young man who is well groomed. He is a son of God, deemed worthy of holding the holy priesthood of God. He does not need tattoos or earrings on or in his body. The First Presidency and the Quorum of the Twelve are all united in counseling against these things." 
 
Here is a link to the talk: 
Ensign Talk

Our bodies are temples. Temples that God created himself.  
Just like with a temple building, you would never mark it, graffiti it, or drill holes into it. The same is with your body. You should never mark your body or put holes into your body. 
I have a friend who is an evangelist and she decided to get a tattoo on the small of her back with a cross and a Psalms scripture on it. She tried to explain to me that it was acceptable to have a tattoo if it expressed your belief and devotion to God. I then explained to her that “Man looketh on the appearance, but God looketh upon the heart.” He knows if you are devoted to Him or not, through your faith, your words, and actions. I am not sure if she took to heart what I said to her but, I still stand by what I said. 
Not to mention, think about what your body would look like when you’re 50+? 
A lot (not all) of tattoos or piercings are also caused by a phase in life. So what if you finally decided to get it removed? All the money and pain to get it removed! 
Our bodies are more of a privilege sent from God, so in reality, our bodies are not essentially "ours." What we do with our bodies is under the order of Him, not only with tattoos or piercings, but with what we take into our bodies (Word of Wisdom), what comes out of our body (clean language), and relations that are saved only for marriage in order to multiply and replenish the earth. 
 
I hope this has helped and brought some consideration. 
Thanks! 
:)

my mormon friend said the body is eternally god's and she's just using it at the moment. I replied "except the ears. the ears are yours," necause she has ear piercings. explain.

The Church does not endorse the non medical application of tattoos and piercings for its members.  
 
We view the body as a sacred temple that houses our spirit and to tattoo or pierce it is a offense to God.  
 
The Church does approve women and young women to have 1 modest set of earrings. But besides that they very strongly oppose all piercings and tattoos.  
 
Having tattoos will not prevent your from joining the Church. In most cases they will expect you to remove all non approved piercings before approving baptism but this is done on a case by case basis. 
 
After joining if you decide to get piercings or tattoos it does not mean you will be excommunicated, though there will most likely be some counseling and/or admonishing done.  
 
Some may find this excessive or unfair but it is done out of respect to the bodies we are given by our God.

I have tattoos. One of them is visible on my ankle. I am seriously considering becoming Mormon. Will this effect my acceptance?

No. Not at all.

I have some tattoos and I see others that have them at church. But you will still run into a few Mormons that still wont have anything to do with you because you do have tattoos. The only bad experience I had with my tattoos was once at a church ball game i was asked to put a shirt on under my jersey to cover my tattoos or leave the court and that was maybe 6 or 7 years ago.

I have 17 tats. My bishop a convert has one. It wont be a issue

i have a few big big tattoos all over my neck arms and i have 5 percings in my face. when i was younger i was baptized mormon and i was also sealed in the temple with my family. well 12 years later i now want to go back to church badly with my husband will i be judged and told to leave the church?? i know in my heart that god loves me and i have taken the wrong path but now i live my life good and just want to go back to church but im afraid they will tell me to leave?

Holi, 
 
There is no problem coming back to church. There will be no reason why you can't even go to the temple. Although tattoos are discouraged, they will not prevent anyone from being baptized, receive the priesthood, go to the temple, etc. 
 
You will probably have to put up with some comments from some members who might be insensitive, but just ignore them. 
 
All are welcome to come to Christ who keep his commandments. No tattoos is not a commandment. It is counsel that should be heeded, but you should feel absolutely welcome in coming.