Even relatively small servers are capable of executing hundreds of queries per second.
Therefore I think that a first, major bottleneck is caused by improper tuning of your Postgres instance. There are a ton of tunable parameters, hop over to PGtune to get a good starting tune.
Then, have a look at your queries. Do you have indexes that cover most queries? Run your queries with explain
(eg in pgAdmin) and see how efficient they are
Then, look whether your queries return appropriate dataset sizes. No need to return an entire table if you just want 1 record. In that case, optimize your queries.
You see, there's a lot you can do before having to turn to more exotic, complicated and often more brittle techniques.
Regarding your comment: specifically for postgres the wiki has some interesting information. Anyways, a healthy dose of reading the fine manual is crucial as well. Database engines are fine pieces of engineering, and you should understand a fair bit of what's going on under the hood to really manage them well. And there's some bad news as well: tuning your database is highly dependent on the size of the database, how and how efficient it is accessed, in real world scenarios you will constantly keep an eye on how it performs and what actions could improve the situation. We use pgBadger for many of the analysis tasks.