Shinkiba station can be reached with the Rinkai line or Yurakucho line

How do I get to SBO/TGS?
The Makuhari Messe venue has an official guide section here, but here's two general ways of getting there, together with maps.

The cheap way:
From Tokyo station, take the Keiyo line to Kaihin Makuhari. 32 - 42 minutes depending on local or express. Once you're at Kaihin Makuhari, exit and go left, then just follow everyone for a 6-8 minute walk to the venue. Train fare costs around 540-620 yen depending on where you're coming from. If you're a SBO contender and you need to hit the venue before the crowds arrive, here's a direction map. Note that there's an escalator to an overhead walkway that you need to take after a few minutes of walk on the streets.

If you want to make sure that your train is on the right track, here's the list of stations it should pass.

Tokyo station can be a bit hard to figure out if you're hitting the show earlier than most other people, but if you're hitting it around the same time as everyone else, it's easy- just follow the otaku looking crowd and you won't get lost. The map below indicates which way you need to go for the Keiyo line platform. Note how the passageway for the Keiyo line cuts off on the map. There's a reason for that. The passageway is a bit long and you'll be walking for about 10 minutes before you can reach the platform. A pdf version of the map can be found at the bottom of the page here.


 

The expensive (but no long walk) way:
From Shinkiba station, take the Keiyo line to Kaihin Makuhari. 22 - 30 minutes depending on local or express. Once you're at Kaihin Makuhari, exit and go left, then just follow everyone for a 6-8 minute walk to the venue. If you're a SBO contender and you need to hit the venue before the crowds arrive, here's a direction map. Note that there's an escalator you need to take after a few minutes of walk from the train station.

Shinkiba station can be reached with the Rinkai line or Yurakucho line.

This expensive method can be good on the way back, especially if you've got lots of leaflets from the show. You'll need to pay two train fares: one for your ride to Shinkiba, and 380 yen from Shinkiba to Kaihin Makuhari. For example, it takes 620 yen to get to the venue from Shinjuku taking the cheap way, but 920 yen taking this expensive way (540+380). For Ikebukuro, it's 690 and 950 (570+380) yen, respectively. The time it takes to get to the venue isn't too different between the cheap and expensive way.
If you want to make sure that your train is on the right track, here's the list of stations it should pass.