RACE can provide the sequence of an RNA transcript from a small known sequence within the transcript to the 5 end (5 RACE-PCR) or 3 end (3 RACE-PCR) of the RNA. This technique is sometimes called one-sided PCR or anchored PCR.
The first step in RACE is to use reverse transcription to produce a cDNA copy of a region of the RNA transcript.  In this process, an unknown end portion of a transcript is copied using a known sequence from the center of the transcript. The copied region is bounded by the known sequence, at either the 5 or 3 end.
The protocols for 5 or 3 RACES differ slightly.  5 RACE-PCR begins using mRNA as a template for a first round of cDNA synthesis (or reverse transcription) reaction using an anti-sense (reverse) oligonucleotide primer that recognizes a known sequence in the middle of the gene of interest; the primer is called a gene specific primer (GSP). The primer binds to the mRNA, and the enzyme reverse transcriptase adds base pairs to the 3 end of the primer to generate a specific single-stranded cDNA product; this is the reverse complement of the mRNA. Following cDNA synthesis, the enzyme terminal deoxynucleotidyl transferase (TdT) is used to add a string of identical nucleotides, known as a homopolymeric tail, to the 3 end of the cDNA. (There are some other ways to add the 3-terminal sequence for the first strand of the de novo cDNA synthesis which are much more efficient than homopolymeric tailing, but the sense of the method remains the same). 
PCR is then carried out, which uses a second anti-sense gene specific primer (GSP2) that binds to the known sequence, and a sense (forward) universal primer (UP) that binds the homopolymeric tail added to the 3 ends of the cDNAs to amplify a cDNA product from the 5 end.
3 RACE-PCR uses the natural polyA tail that exists at the 3 end of all eukaryotic mRNAs for priming during reverse transcription, so this method does not require the addition of nucleotides by TdT.  cDNAs are generated using an Oligo-dT-adaptor primer (a primer with a short sequence of deoxy-thymine nucleotides) that complements the polyA stretch and adds a special adaptor sequence to the 5 end of each cDNA.  PCR is then used to amplify 3 cDNA from a known region using a sense GSP, and an anti-sense primer complementary to the adaptor sequence.