Hi there,
As the others have said, there's no passenger service to Las Vegas.
If you absolutely have to get there by rail then you're going to have to do a hobo impression and jump onto a freight train.
Sounds fun but probably a really bad idea to actually do!
A more sensible approach is getting the coach from Bakersfield or LA.
An alternative sensible approach is to get the train to Burbank (on the outskirts of LA) and then fly from Burbank airport to Las Vegas. Southwest are currently offering about 8 or 9 flights a day for $60 per person each way.
I've done the transfer between the train and airport at Burbank. It's not far at all and there was a free stuttle between them which took about 2 minutes. I think you can walk it but there's a busy road to cross.
Enjoy your trip, I've done some great US train trips and I'd recommend it.
Cheers,
Jason