I have a question based off the edgeR handbook.  I

In the hand handbook it explains setting up contrasts as follows:

my.contrasts <- makeContrasts(
DrugvsPlacebo.0h = Drug.0h-Placebo.0h,
DrugvsPlacebo.1h = (Drug.1h-Drug.0h)-(Placebo.1h-Placebo.0h),
DrugvsPlacebo.2h = (Drug.2h-Drug.0h)-(Placebo.2h-Placebo.0h),
levels=design)

The handbook then says:

To find genes that have responded differently to the drug and the placebo at 2 hours: 

lrt <- glmLRT(fit, contrast=my.contrasts[,"DrugvsPlacebo.2h"]) 

My question is how to interpret the up and down regulation. If there are differentially up-regulated genes resulting from this contrast set-up, is it appropriate to say that these genes are up-regulated in response to the drug compared to the placebo at 2 hours?

No, you have to look at the underlying data. In other words, your DrugvsPlacebo.2hr is literally computing

(Drug.2h-Drug.0h)-(Placebo.2h-Placebo.0h)

and then testing to see if there is evidence that the resulting value is different from zero. But there are any number of ways that you can get something different from zero.

1. Big difference for drug treatment, no difference for placebo
2. No difference for drug treatment, big difference for placebo
3. Up-regulation in drug treatment at 2 hrs, down-regulation in placebo at 2 hrs
4. Down-regulation in drug treatment at 2 hours, up-regulation in placebo at 2 hours
5. Up-regulation in drug treatment, smaller up-regulation in placebo
6. Down-regulation in drug treatment, smaller down-regulation in placebo

Usually for this sort of thing I like to use ReportingTools and make HTML tables, with little plots that show the relative differences, so people can see at a glance what is going on.