Isolate mRNA from eukaryotic cells by lysing cells and making use of the fact that at the 3' end of nearly all eukaryotic mRNAs there is a stretch of 50 - 250 adenylate residues  the polyA tail. This allows them to be purified away from the more abundant tRNAs and rRNAs.
 

Purification can be performed by binding mRNAs on a solid matrix to which short strings of thymidylate residues are attached (oligo dT matrix). The mRNAs are removed again by washing in a low salt buffer.

 To convert the mRNA into cDNA, we have to go through a number of steps:

Fig 7-15 Lodish et al, 4th ed

First strand synthesis requires the use of reverse transcriptase (a viral enzyme) and an oligo dT primer.
The enzyme terminal transferase adds nucleotides to the 3' end of single- or double-stranded nucleic acids (without requirement for a template).
If only one nucleotide is provided (e.g. dGTP) then a homopolymeric tail is added to the 3' ends of the duplex.

To prepare the cDNA for cloning, a number of further steps can be taken. The cDNA ends can be made flush by treating with a single strand specific nuclease (e.g. S1 nuclease) to remove 3' overhangs, and Klenow enzyme to fill in any missing 3' nucleotides. At this stage, can ligate the cDNAs by blunt-end ligation. However, we can also ligate linkers to either end of the cDNAs using DNA ligase. Thelinkers are short oligonucleotides incorporating restriction enzyme sites (e.g. EcoRI). If the 5' ends of the linkers are not phosphorylated, only one can be added to each cDNA end. The cDNAs can then be digested with EcoRI to leave cohesive ends for efficient cloning into an EcoRI-digested vector.