Basic Notions (Darwin, 1859):

1.  Natural Variation:  There is variation for just about any characteristic in any characteristic of sexually reproducting organisms.  Much of this variation has a GENETIC basis.  THIS WAS NOT CONFIRMED UNTIL THE WORK OF MENDEL BECAME GENERALLY KNOWN - CA. 1900.

2.  Differential Survival:  All progeny do not live to reproductive age, i.e., is a given plant population, all seeds produced by one generation do not survive to contribute to the next generation.

3.  Generational change in gene frequencies:  Individuals within a population that carry 'favorable' characteristics are more likely to survive to reproductive age than those that do not.  Those that carry 'unfavorable' characterists are least likely to survive to reproductive age.  If these characteristics have a genetic basis (Mendel demonstrated that most do) then, through NATURAL SELECTION, sequential generations will carry MORE favorable characteristics and LESS unfavorable characteristics, i.e. natural selection works to CHANGE gene frequencies with each generation.
 

Examples of directional selection:  human-imposed positive pressures ('artificial' selection) to produce domesticated animals and plants over the past 20,000 years and human-imposed negative pressures to produce various types or organisms resistant to chemical-based eradication efforts.  Regardless of source, selective pressures act on genetic variation this is expressed at various levels:
 

• 'point' gene mutation (nucleotide sequence change - red, white, pink flowers)
• genomic or chromosomal mutation
• polyploidy (multiple genomes - common in flowering plants)
• aneuploidy (loss or gain of chromosomes)
• structure of individual chromosomes (gene positional changes)
• recombination (gene flow/hybridization)
• allogamy (max variation via meiotic recombination - 'liberal')
• autogamy (minimal - 'inbreeding' - conservative)
• apomixis (vegetative propogation or agamospermy - 'fixing' the genome)