Taxi from Shinjuku to Shinokubo Station

I'm going to be staying near Shinokubo Station and I'll be taking the N'EX to Shinjuku Station. I don't want to bring all my luggage on the Yamanote line even though I know it would be much quicker and cheaper. I'd rather get a taxi directly to my hotel so I don't have to deal with being in the way on the train with both my brother and I's luggage.
Where would I find a taxi from the N'EX platform at Shinjuku Station? Also how do I take the taxi, like how do I communicate that I want to ride in their taxi? Will they be waiting for customers?

Where would I find a taxi from the N'EX platform at Shinjuku Station?

There are taxi stands at the station exits.

Also how do I take the taxi, like how do I communicate that I want to ride in their taxi?

Walk up to the first taxi in line at the taxi stand. The driver will open the door for you. He'll also help you with your luggage.

Depending on where your hotel is, expect it to cost around 1000 yen for the taxi ride.

More general taxi info here:

http://www.japan-guide.com/e/e2021.html

Is there taxis at every station exit?
Which exit would be the most convenient for catching a taxi to Shinokubo?

Take Yamanote line easiest except weekday rush hours.
Platform from [6] to [15] not needs ticket gate out same JR-East rail both.
http://www.jreast.co.jp/estation/stations/866.html

It depends on where exactly you exit, but the major exits have taxi stands just outside. Minor exits are not always immediately near a street but you can usually flag one down pretty easily.

I'd recommend shooting for the South Exit. There's a taxi stand there and its reasonably easy to get to Shin-Okubo from there.