Chainsaw and Stump Grinder
If you only need to remove one or two trees the easiest and most cost efficient method is with a decent chainsaw and stump grinder. After cutting the tree down in the usual way, grind the stump into sawdust with the stump grinder. This frees up space for planting, as well as eliminates the eyesore of stumps.
Bulldozing and Burning
Using a bulldozer to slam into trees, ripping them out of the ground and pushing them into a big pile to be burned or hauled off, has been the tried and true method of dealing with cedar removal on a large scale for many years. The bulldozer can literally pull small trees out of the ground like a person pulling weeds by hand. Larger trees get sheared with a special blade attachment that hooks onto the front of the machine.
Bulldozing gets the job done quickly, relatively cheaply but not without some environmental impacts. The heavy machinery can leave ruts in the ground, some of which may injure the roots of other desirable trees in the area. Then there is the carbon foot print of burning huge piles of waste wood or having it hauled off in big trucks -- but you will mostly eliminate the stumps and roots, making planting something else a lot easier.
Forestry Mulchers
A relatively new method of removing cedars is the use of forestry mulchers. These machines shove a fixed teeth rotor into the trees, cutting and chopping them to ground level, creating a mulch that is left behind to improve soil water retention. The manufacturers claim that soil impaction is less than a human foot would make. This machine can easily maneuver into tight areas with no damage to other trees or shrubs.
Options
The chainsaw, bulldozer and forestry mulcher are all excellent tools for removing unwanted cedars. Two considerations to keep in mind are how much you want to spend on the project and how do you want the area to look afterwards. Bulldozing is initially more destructive but it clears out most of the stumps and roots, making future planting a lot easier. The forestry mulcher is gentler on the land, but leaves stumps (at ground level) and a layer of mulch over the area.