What part of food gives the blood red color?
The red colour of blood isn't actually to do with food at all.  The primary purpose of the blood is to carry oxygen to all the cells that require it to release energy.  Red Blood Cells are filled with an iron containing pigment called haemoglobin.  When it has oxygen bonded to it, haemoglobin  has a bright red colour - it is this that gives blood its red colour.

In terms of how food enters the bloodstream, it is first broken down into extremely small constituents.  This is done by mechanical action (i.e. chewing and the squeezing movement of your digestive system) and by chemical action through the use of enzymes.  Enzymes are proteins that are secreted by various glands in the mouth (and are therefore contained in saliva), stomach and both intestines.  These chemically break large food molecules down into small products such as glucose (sugar) and amino acids (protein-building blocks) amongst other things.  These then move across the wall of the intestines and into the bloodstream, which are separated by only one cell:



Unfortunately that's the best image I could find.  The intestine is everything outside of the pink layer (which is the wall of the intestine).  The small molecules are able to pass through the pink layer and straight into the blood stream.  The picture shows a fold in the wall of the gut, which increases its surface area so allows more molecules to diffuse across.