A design that concisely models your problem is always a good start. Overgeneralizing the data model can lead to performance problems. For example, I've heard reports of projects striving for uber-flexibility that use the RDBMS as a dumb "name/value" store - and resulting performance was appalling.
Once a good design is in place, then use the tools provided by the RDBMS to help it achieve good performance. Single field PKs (no composites), but composite business keys as an index with unique constraint, use of appropriate data types, e.g. using appropriate numeric types for numeric values rather than char or similar. Physical attributes of the hardware the RDBMS is running on should also be considered, since the bulk of query time is often disk I/O - but of course don't take this for granted - use a profiler to find out where the time is going.
Depending upon the update/query ratio, materialized views/indexed views can be useful in improving performance for slow running queries. A poor-man's alternative is to use triggers to invoke a procedure that populates the table with a result of a slow-running, infrequently-changed view.
Query optimization is a bit of a black art since it is often database-dependent, but some rules of thumb are given here - Optimizing SQL.
Finally, although possibly outside the intended scope of your question, use a good data access layer in your application, and avoid the temptation to roll your own - there are surely tested and performant implementations available for all major languages. Use of caching at the data access layer, middle tier and application layer can help improve performance considerably.