This is most obvious in the case of processed pseudogenes derived from eukaryotic protein-coding genes so that's the example I'll describe first.
In the example below, I start with a simple, hypothetical, protein-coding gene consisting of two exons and a single intron. The gene is transcribed from a promoter (P) to produce the primary transcript containing the intron. This primary transcript is processed by splicing to remove the intron sequence and join up the exons into a single contiguous open reading frame that can be translated by the protein synthesis machinery (ribosomes plus factors etc.).1 [See RNA Splicing: Introns and Exons.]
Processing includes modifications to protect the mRNA from enzymes that attack the ends of unmodified RNA molecules. A cap is added to the 5′ end and a polyA tail consisting of a stretch of 50-100 adenylate residues (A) is added to the 3′ end.
Occasionally, the mature mRNA will be accidentally copied by reverse transcriptase to produce an RNA:DNA double-stranded molecule. Reverse transcriptase enzymes are ubiquitous but they are much more common in cells with large genomes harboring retrotransposons and integrated retroviruses. Both of those elements contain genes for reverse transcriptase.
When the RNA is degraded, the single stranded DNA molecule can be copied by DNA polymerase to produced a double-stranded DNA molecule that is complementary to the original mRNA molecule. This is complementary DNA, or cDNA. One of the characteristics of this molecule is that it contains a stretch of A/T base pairs at one end revealing that it was formed from an RNA molecule.
If the cDNA gets accidentally integrated into the genome then it becomes a processed pseudogene. The integration event (recombination) results in a short duplication of target DNA at the site of integration. This is a characteristic of processed pseudogenes.
Integration can occur almost anywhere in any chromosome although there is an obvious preference for regions consisting of "open" chromatin where the DNA is more exposed. That's why processed pseudogenes are more likely to be present near genes that are expressed and they're much less likely to be found in heterochromatic regions. As a general rule, processed pseudogenes are not located anywhere near their parental gene. This is one of the features of processed pseudogenes that distinguish them from pseudogenes derived from gene duplications
One of the other main distinguishing characteristics of the processed pseudogenes that are derived from protein-coding genes is that they lack a promoter and so they are not transcribed at anywhere near the same level as the parental genes. They will be transcribed by accident (spurious transcription) just like all the other junk DNA sequences but that's very low level transcription.
This isn't true for many processed pseudogenes derived from genes for functional noncoding RNAs. Most of those genes specify small RNAs and they are transcribed by RNA polymerase III in eukaryotes [Eukaryotic RNA Polymerases ]. The promoters in such genes are "internal"—they are found within the sequence that is transcribed. These are called "Class III genes" and you can read how one of them, the 7SL gene, is transcribed at: Transcription of the 7SL Gene. This is the transcript that gives rise to the million Alu sequences in your genome.
This pseudogene has a promoter so it can be transcribed by RNA polymerase III to produce more RNAs. Transcription will not be regulated as carefully as it is with the parent gene because the parental gene is associated with additional upstream regulatory sequences. This pseudogene quickly acquires mutations that render the RNA product nonfunctional.
This type of pseudogene can expand within a genome by producing more and more copies. If one of those copies lands near sequences that enhance integration then the new element can propagate even more rapidly by another mechanism. The best-studied example is Alu elements in the human genome (Deininger, 2011) [see animation at: How Alu jumps]. This seems to be what happened in the lineage leading to humans.
Several thousand new Alu elements have become fixed in the human genome since the divergence of humans and chimpanzees suggesting that the frequency of new insertions in the germ line cells is quite high.
In single-cell eukaryotes, the newly integrated pseudogene can be passed on directly to the daughter cells whenever the parental cell divides. In multicellular species, the cells in the lineage derived from the parent cell will all carry the pseudogene in one of the two chromosomes passed on to the daughter cells but the offspring of that individual will not inherit the pseudogene unless it arose in the germ line cell lineage. In the humans this means that the new pseudogene has to be present in sperm cells or egg cells.
Some genes have lots of processed pseudogenes while other normal genes have none. The number of pseudogenes is related to the abundance of the parental RNAs in germ line cells, just as you would expect. Housekeeping genes, which are expressed in all cells, are far more likely to spawn pseudogenes than genes whose expression is highly restricted to non-germ line tissues (Podlaha and Zhang, 2009; McDonell and Drouin, 2012). This is why there are many different processed pseudogenes derived from the genes for standard metabolic enzymes, the genes for ribosomal proteins, and the genes for snRNAs (spliceosomal RNAs).
But just because the new pseudogene is created doesn't mean it will become fixed in the genome of every individual in the species. That process can only occur by a mechanism that allows fixation of a non-functional piece of DNA that's effectively neutral with respect to selection. That process is, of course, random genetic drift.
This leads to the conclusion that millions of processed pseudgenes are formed for every one that becomes fixed. That may sound like a lot but over the course of million of years in a population of tens of thousands of individuals—as in the human lineage—the formation of a processed pseudogene in a germ cell is still a rare event.
The exons at the ends of genes will also contain noncoding regions at the 5′ and 3′ ends. They are required for translation initiation and termination and for polyadenylation (and other things). I've ignored them in order to simplify the description. We could draw the gene like this (below) where the dark blue region is the coding region and the open blue boxes at either end represent the 5′ untranslated region (UTR) on the left and the 3′ untranslated region on the right.
Deininger, P. (2011) Alu elements: know the SINEs. Genome Biol, 12(12), 236. [doi: genomebiology.com/2011/12/12/236]
McDonell, L., and Drouin, G. (2012) The abundance of processed pseudogenes derived from glycolytic genes is correlated with their expression level. Genome 55:147-151. [doi: 10.1139/g2012-002]
Podlaha, O., and Zhang, J. (2009) Processed pseudogenes: the ‘fossilized footprints’ of past gene expression. TRENDS in Genetics 25:429-434. [doi: 10.1016/j.tig.2009.09.002]