TL;DR (Too Long; Didn't Read)
Make sure that the repair service you choose is legitimate and qualified. If their website doesn't convince you, search online for articles written about their company. If you're still skeptical, call or email the listed representative and ask as many questions as you need.
Don't attempt to refill your snow globe on your own. If you damage it further in the process, repairs can be more costly.
Although it's tempting to find a fix-it-yourself solution to every problem, sometimes it is necessary to seek additional help. Snow globes are fragile and, therefore, difficult to refill on your own. Also, they contain a combination of glycerin and distilled water, which is hard to recreate from home. If your precious snow globe's liquid evaporated or turned cloudy, you can restore it to pristine condition with a professional's assistance.
Search for snow globe repair professionals like Herb Rabin's Snow Dome Repair Service and Ferrara Studios Snow Globe Repair and Custom Snow Globe Service. Check out the available services for each of your options to ascertain that they offer refills as well as repairs. Look at any before and after pictures to get an idea of the quality of their repair work.
Compare the refilling costs for each repair service that you find. Determine how much shipping costs and choose the most reasonably priced option. Decide on a method of payment.
Package your snow globe in bubble paper to ensure that it isn't damaged further en route. Send in your snow globe to the address listed for repairs.