You can use the stream-to module, which can convert a readable stream's data into an array or a buffer:
var streamTo = require('stream-to');
req.form.on('part', function (part) {
    streamTo.buffer(part, function (err, buffer) {
        // Insert your business logic here
    });
});
If you want a better understanding of what's happening behind the scenes, you can implement the logic yourself, using a Writable stream. As a writable stream implementor, you only have to define one function: the _write method, that will be called every time some data is written to the stream. When the input stream is finished emitting data, the end event will be emitted: we'll then create a buffer using the Buffer.concat method.
var stream = require('stream');
var converter = new stream.Writable();
// We'll store all the data inside this array
converter.data = [];
converter._write = function (chunk) {
    converter.data.push(chunk);
};
// Will be emitted when the input stream has ended, 
// i.e. no more data will be provided
converter.on('finish', function() {
    // Create a buffer from all the received chunks
    var b = Buffer.concat(this.data);
    // Insert your business logic here
});