enolate alkylation

Here is the most direct way to grow a carbon chain at the alpha-position. Make the enolate with a base, then add an alkyl halide. The carbon end of the enolate, acting as a nucleophile, attacks the carbon of the alkyl halide in an SN2 reaction, kicking out the halide and forging a brand-new carbon-carbon bond. A hydrogen on the alpha-carbon has effectively been swapped for an alkyl group.

Because the key step is SN2, the usual SN2 rules apply to the electrophile: methyl and primary alkyl halides work well, secondary ones are sluggish, and tertiary halides fail entirely (they would rather eliminate). The enolate is a strong base as well as a nucleophile, so bulky or hindered electrophiles tend to give elimination instead of substitution. Reactive electrophiles like allylic and benzylic halides, or alpha-halo carbonyls, are especially good partners.

With a simple, unsymmetrical ketone there is a catch: you must control WHICH enolate forms and avoid making a mixture, and you must avoid alkylating twice. The clean solution is to use a strong, bulky, non-nucleophilic base like LDA at low temperature, which deprotonates completely to give a single, well-defined enolate (usually the kinetic one) before the electrophile is added. For the special case of doubly-activated substrates — malonic and acetoacetic esters — alkylation is far easier, which is exactly why those synthon strategies are so popular.