I second the bus if you're not familiar but if you most get the train then this might help.

I've only ever been past the Intercon on the Monorail (btw, I recommend crossing the Rainbow bridge by Monorail by day or night) so I think the following route will work:

i) Get the NEX to Tokyo station.
ii) Jump on the Yamanote loop line in the direction of Yurakucho.
iii) Jump off at Shimbashi and follow the directions to the Yurikamome line (this appears to terminate at Shimbashi).
iv) Get the first monorail train that comes along.
v) Jump of at Takehiba - a passage links this to the Intercontinental.

Ticketing for NEX, Yamanote and Yurikamome will be separate..

The following links might be useful:

http://www.jreast.co.jp/e-info/map_a4ol.pdf
http://www.yurikamome.co.jp/english/index.php#en00

(print the first map out on A4 paper in colour - I found this useful for getting around)

Oddly enough, the Yurikamome line doesn't appear on any of the Japan Rail maps I've seen so it's probably a separate company.

Oh, and while we're at it, I know cross posting is frowned upon round here but I'm sure no one will object if you post the same question on the Tokyo forum.

Edited to add: in terms of taxi, Hamamatsucho station is probably a little closer (about 30 minutes walking from the Intercon).