Alright, so let's first start with making the distinction between Javascript in a web browser, and Javascript on a server (CommonJS and Node).
Javascript is a language traditionally confined to a web browser with a limited global context defined mostly by what came to be known as the Document Object Model (DOM) level 0 (the Netscape Navigator Javascript API).
Server-side Javascript eliminates that restriction and allows Javascript to call into various pieces of native code (like the Postgres library) and open sockets.
Now require() is a special function call defined as part of the CommonJS spec. In node, it resolves libraries and modules in the Node search path, now usually defined as node_modules in the same directory (or the directory of the invoked javascript file) or the system-wide search path.
To try to answer the rest of your question, we need to use a proxy between the code running in the the browser and the database server.
Since we are discussing Node and you are already familiar with how to run a query from there, it would make sense to use Node as that proxy.
As a simple example, we're going to make a URL that returns a few facts about a Beatle, given a name, as JSON.
/* your connection code */
var express = require('express');
var app = express.createServer();
app.get('/beatles/:name', function(req, res) {
var name = req.params.name || '';
name = name.replace(/[^a-zA_Z]/, '');
if (!name.length) {
res.send({});
} else {
var query = client.query('SELECT * FROM BEATLES WHERE name =\''+name+'\' LIMIT 1');
var data = {};
query.on('row', function(row) {
data = row;
res.send(data);
});
};
});
app.listen(80, '127.0.0.1');