Since your hair is fine, it is likely much harder for you to secure the tiara and veil. This means more of a base to anchor to. Using more, smaller bobby pins will help (versus larger hair pins, which tend to slide out easier). Also consider a metal veil comb, instead of the standard plastic. It will hold pins better. After securing the comb in your hair, pin the comb to your hair. Experiment with hair piece clips as well (the kind that hold hair extensions onto shorter hair). These actually clamp onto your hair instead of simply sliding in.
Some tiaras are actually attached to combs, so you can use similar methods to hold these in place. To avoid having to worry about the tiara and veil separately, you can get a tiara comb and sew the veil to it (in much the same way a veil attaches to a plain veil comb). The disadvantage to that approach is you cannot remove the veil without also removing your tiara.