It may make both you and your kid a little squeamish, but it's best to take your child's temperature rectally until age 3 or so. That's because it's the most accurate, and with babies and toddlers, even small differences in temperature can affect how serious a fever is or whether to call/see the doctor. But after this age, you can try other types of thermometers, like axillary (under the arm), tympanic (in the ear), or oral (in the mouth). If you go the oral route, make sure your child knows not to bite it, which can skew the results. Whatever type of thermometer you choose, be sure to pick a digital one, which can give you a reading in a minute or less, depending on the brand, which is key when you have a toddler who won't sit still.
To use a digital thermometer, first be sure it's clear of old readings. If your thermometer uses plastic sheaths, place a clean one over the tip and take your child's temperature per the directions. Give your pediatrician a call if your child is under 3 months and has a fever of 100.4 F. or higher, is between 3 and 6 months old and has a fever of 101 F. or higher, or is older than 6 months and has a fever of 103 F. or higher. When you're done, toss the plastic sheath (reusing them can skew the next reading).