Passed and Past are two words that are often mixed up, because they can be used in a very similar manner. Remember:
He walked past something; or, he passed something.
Past, in this usage, is an adverb which must be used in conjunction with a verb. Past will always have a verb with it when being used to describe movement.
Passed is the past-tense form of the verb "to pass," and will not be paired with a verb. If you don't have another verb (like "walked" or "drove"), you may use passed.
So, in review:
Wrong: She walked passed the table without looking at him.
Right: She walked past the table without looking at him.
Wrong: She past the store and had to double back.
Right: She passed the store and had to double back.