Personally, I prefer using a shuttle service whenever I make that trip. But what works best for you depends on your situation, your priorities, and your logistics. For example, if you are traveling as part of a group, then splitting the bill for a shuttle service might be cheaper than all other options.
As far as other options go, flying is the fastest way to get to Vail. And while there is not an airport in Vail, you can fly to Eagle County Regional Airport, which is located about 40 miles west of Vail. For comparison, the trip from Denver International Airport to Vail is 120 miles long, through roads that are often full of traffic during skiing season. Arriving from the West via the I-70 can spare you from some of that traffic.
You can also rent a car and drive yourself from Denver to Vail. That will leave you to contend with the traffic and the snow-covered roads, but that’s not a major problem. The main reason people don’t drive to Vail is parking, which is often quite expensive. And since you won’t be driving inside Vail, renting a car is likely not worth the investment. Not unless you plan to explore the surrounding areas, or stay in a town outside of Vail.
There is a bus that goes from Denver to Vail. That’s the cheapest method to go there, but it does require that you go from the DIA to Union Station, which is located downtown, 25 miles away from the Airport.
Or you can use a shuttle service. Like I said, this is my favorite option. You get comfort and speed, and the prices are usually better than going by plane. I use the same method when going from Vail to Aspen. In fact, shuttle services are a great way to get anywhere in the Rocky Mountains.