Indoors is hard and you pretty much have to accept that you will get some noise unless you can afford really high spec gear. A noisy shot is better than a blurry shot though!
Shooting in RAW can help you in post to reduce the colour noise and clean up the image a bit more.
1/400th Sec, ISO 400, 50mm, F2
1/125th sec, ISO200, 50mm, F2
1/250th sec, ISO400, 50mm, F2
1/250th sec, ISO400, 50mm, F2
Those above where all shot in Clogher Valley MCC which has relatively good lighting for an indoor venue thus allowing lower iso's when you stop down to f2.
1/200th sec, ISO1600, 10mm, F4
1/400th sec, ISO1600, 94mm, F4
1/200th sec, ISO1600, 10mm, F4
The last 3 shots where taken in the Naul in Dublin, the lighting is similar to CVMCC but as the track is much bigger access is more restrictive meaning the 50mm would not work out as well as it does indoors on the smaller track. To combat this I used my 10mm to take wide field shots showing a car and the track as a whole to help give some context. The one close up shot of the car displays quite a bit of noise but with my 70-200 f4L that was sadly unavoidable due to simply there not being enough light/my camera not being sensitive enough to light/my lens not having a large enough aperature. A noisy picture is still better than none at all though.