Roughly, what I know is, when we eat food it goes into our: Stomach > Small Intestine > Large Intestine > Rectum. So, it just moves through a digestive pipe.
What I don't understand is, what part of the food is responsible for blood's color and how does the food that we eat mixes with blood?
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.
In essence, some of your food contains iron (especially red meat). This is taken up by your body and integrated into the haemoglobin protein which red blood cells contain in high amounts.
The iron in haemoglobin can bind oxygen (it does this when it passes through the lungs) which enables the red blood cell to carry it through your blood circulation.
The colour of blood comes from this haemoglobin. When the iron is binding oxygen, it is red. Otherwise, blueish-red. (http://www.ebi.ac.uk/interpro/potm/2005_10/Page1.htm)
Ingested food is digested within the digestive canal. This means that it is broken down into smaller molecules that are then transported into cells lining the digestive canal (by proteins that expend energy to do this). The nutrients are then further transported until they reach blood vessels (or, in the case of lipids, lymphatic vessels, which eventually empty into veins). However, the 'pigment' that gives blood its red color is generally constructed from smaller molecules and atoms within the body, and not directly acquired from food.
Ultimately, the red hue in human blood is due to a protein known as hemoglobin. Each hemoglobin protein is bound to four 'heme' molecules, and each of these are in turn bound to a Fe2+-ion* (a form of iron) and either O2 (oxygen) or CO2 (carbon dioxide). All of these components are required to give hemoglobin (and thus blood) its distinct hue.
The molecules derived from food that are used to build the complete hemoglobin complex are:
Used to synthesize the actual hemoglobin protein. Obtained from dietary protein, as free amino acids, or (in the case of non-essential amino acids) synthesized from other molecules.
Used together with glycine (an amino acid) to synthesize heme. Most succinate is derived from lipids (e.g. fatty acids), carbohydrates or amino acids in food.
Obtained from a variety of dietary sources.
Mainly produced at the final step of aerobic energy production where mitochondria break down carbohydrates, lipids or amino acids to form water, CO2 and chemical energy.
Almost exclusively obtained from the air via direct absorption in the lungs.
For more information on how proteins such as hemoglobin are synthesized from amino acids, you could see e.g. this video. For more information on metabolic pathways, I suggest having a look at this map. In the latter, you can focus on human metabolic pathways by unchecking "Unicellular organisms & Fungi" and "Higher Plants" in the menu. It should be noted, though, that this only describes metabolic pathways, and does not go into much detail in terms of how these processes actually work.
*Except in the case of methemoglobin, which has bound a Fe3+-ion and cannot bind O2.
