I always use pliers to grab the handle and twist. Easier on the fingers. There is a lot of pressure when the filter is in properly. This pressure releases when you turn off water flow when you change the filter (most people don't because the valve is inconvenient and it only takes 3 seconds to change a filter). Because it requires some force to put the replacement filter in, for the same reason, I also use pliers to push and turn when replacing the filter. I'm assuming here that your fridge has the tube/cylinder filter. If it does not, ignore everything I just said.
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Shut the water off, then use the water spout to fill a glass of water until you empty the line of your refrigerator. Now you should easily be able to remove the filter and place a new filter in. Once that's done, go ahead and flush the water through using the water dispenser. Side note: it might be easier to shut off the water using the outside shut-off valve that most homes have; for example, mine is in my front yard where my water spigot is.
