To whip up a human clone, doctors would most likely use a process called somatic cell nuclear transfer -- the same technique they've used successfully with animals like Dolly, the famous (and now departed) sheep clone.
In regular old human reproduction, sperm fertilizes an egg, combining two sets of DNA into one. Cloning, however, destroys the existing nucleus in the egg and replaces it with the nucleus from the single clone parent. The vast majority of the resulting egg's DNA would come from the clone parent, though a little bit would still come from the original egg.
Next, doctors would implant the egg in a surrogate mother's womb. Here, in the comfort of a stranger's bun oven, the tiny clone would continue to develop, influenced by environmental factors such as a pack-a-day Pixy Stix addiction and cross-country Phish fandom.
So would having a clone be like having an identical twin? Genetically, the answer is a resounding "sort of." Practically speaking, the answer is "no way." The age difference between twins is generally a matter of minutes, not decades.
Having a clone would be more like having a baby -- though you might be able to talk it out of a donor organ or two when he or she is older.