An extra chromosome is due to nondisjunction. This is when, during meiosis, homologous chromosomes fail to segregate. The result is one gamete has a missing a chromosome (called a monosmy) while the other has an extra (trisomy).
The question posed is pretty broad because humans have 23 pairs of chromosomes, so it really depends which pair has the extra chromosome. However, if we look at some more common trisomies we can start with Trisomy 21 also known as Down's syndrome. Typical signs/symptoms of this disorder include delayed physical development, impaired cognitive/intellectual ability, and recognizable physical characteristics of the face.
Klinefelter's syndrome is when a male has an extra X sex chromosome (genotype XXY). These individuals will have poor muscle tone and in general weak secondary male sex characteristics due to low testosterone. They may also experience infertility.
There are other trisomy disorders such as trisomy 18 or Edward's Syndrome in which most individuals do not survive complications from the disease. So once again, it truly depends on which trisomy is being examined when evaluating how it effects an individual.