Hi! I am really new to modeling and blender. This is my first project, and when I render my model I get some artifacts. here is a blend file and a rendered image. Please help.
www.panline.net/~fabijan/crvena_bivikla.rar
You duplicated the item now there are 2 objects at the same place with gives that strange black thiny. Just select he bike and delete it you will see there is another on it.
Matt
No. its not that, if you download blend file you will see. 
well actually you have duplicated the meshes and the fact that they are overaping is what causes the artifacts as they fight for who should be rendererd. 
for each piece select it go into edit mode select all the vertices then in editing menu choose remove doubles then your problem will be fixed. 
I took a look at your blend. It’s actually a combination of what the previous couple of posters mentioned.
Some of your meshes have been duplicated and you need select the objects, go into edit mode, select all vertices, and remove doubles (w key).
Some of your objects (like the wheels and the rear tire) are duplicated. Select and delete.
nice looking bike
you have a duplicate it might be a seperate object and, or just duplicated verts. Take a look at the outliner in cases like this.
the red shows the outliner icon on the window type menu. take a look at this to see what is realy in your sceene.
I also looked at your blend and what stedfast said would work just fine. 
I did that and rendered it… looked fine to me.