Pixelated photo

I have photos from my Canon 50d downloaded on my computer. I am trying to make a thank you card 4x6 with the photo smaller in the centre. The photo is clear and then I change the background and then resize it. It then is very fuzzy. I just can't seem to figure out what I am doing wrong??? Any suggestions would be great????
Just my first post...pls. be gentle...;)

what format is the picture

It is a jpeg file. 5.6mb. Is this what you need?

When you say change the background,are you refering to adding another image to it?
As far as format goes jpg is fine (should be)Ithought may have save it as .gif. That would do it.Can you tell us the process you use to resize

I will try to explain (in my rookie way) what I was trying to do. I took a photo of a group of people. I tried to resize it smaller in 2 different way. I just cropped it to fit in the middle of a 4x6 photo and I tried to just shrink the image. I thought that 72dpi that it was would be ok for that size of photo. The background was terrible so I put another background underneath. I then erased around the edges to give a nicer background. I then took that redone photo a placed it on a black background to print some thank you words on. I printied out one, and it was totally pixelated. I have redone it and upped the dpi to 500 and it is clear. What caused this? I am just trying to understand what I did wrong. I hope all of this rambling helps you to understand what I was trying to do.

http://www.google.com/search?client=safari&rls=en&q=printing+dpi+requirements&ie=UTF-8&oe=UTF-8
check out a few of those you'll get a better understanding for print requirements verse devise (computers screen,cell phones etc etc) requirements