The basic unit of a polynucleotide chain is the nucleotide.  Click to see bigger picture.

There are two different kinds of sugars in a nucleotide, deoxyribose and ribose.  If the polynucleotide chain forms DNA then the sugars in its nucleotides are deoxyribose while nucleotides containing ribose as its sugar form RNA.
 
There are five different bases in a nucleotide.  These bases are adenine, cytosine, guanine, thymine, and uracil.  Uracil is only found in RNA, while thymine is only found in DNA.  Each base is identified by the first letter in its name.
 

A section of a polynucleotide chain with each individual nucleotide bonded together.  Click on the picture for a better view.

Nucleotides bond together in a chain to form polynucleotide chains such as the one below.  In a polynucleotide chain, there are open ends.  The open phosphate end is called the 5' end while the open sugar end is called the 3' end.
 
 
 
 

A DNA strand consists of two polynucleotide chains bonded together by their nitrogenous bases, thus one looks like this.

 

Typical DNA strand with a nucleotide chain bonded with another.  Click on the picture for a better view.

When scientists were trying to figure the structure of the DNA strand, they came across a problem.  They knew that the bases in DNA were Thymine, Guanine, Cytosine, and Adenine, but they did not know how to fit the chains together.  Adenine and Guanine are both called purines and have the same structure.  Cytosine and Thymine are pyrimidines and have a smaller structure than the purines.  Scientists thought that there were ten different ways the bases could pair up for the DNA strands.
 

There was a problem with the model, though.  The sides of the DNA strands would have to be curved in and out to accommodate for the larger purines to be paired together and the smaller pyrimidines to pair together.
 
Then by examining the structure scientists narrowed the base pairs down to four:  A-C, A-T, G-C, or G-T.  One Purine would pair up with one pyrimidine thus making an even structure.  Two of these pairs were the answer.  This is where the research of a man named Erwin Chargaff came into play.  He had made a discovery that had led to Chargaff's Rule:  A=T, G=C.  By using Chargaff's rule two scientists named Watson and Crick discovered that Thymine paired with Adenine and Guanine with Cytosine.  They also discovered that a hydrogen bond was obtained when the bases were paired together in this way.
 

A Point to Ponder    
In Geometry complimentary angles can be placed side by side to form a right angle.  Base pairs are like complimentary angles.  Just as a 50 degree angle is complimentary to a 40 degree angle - Adenine compliments Thymine and Guanine compliments Cytosine.  In a DNA strand Adenine is always paired with Thymine, and Guanine is always paired with Cytosine.

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