Before you begin installing the new belt, compare it to the old one to ensure it is the proper length and width.  Different vehicles have different sized belts and installing the wrong size could result in failing to power the accessories or even damage to the engine.    If your old belt was loose because it had stretched over time, take that into consideration when comparing the two belts. Make sure both belts have the same number of “ribs” or threads spanning the width of the belt. Using a diagram or the picture you took to guide you, snake the new belt around all the necessary accessory pulleys except the auto-tensioner or alternator (depending on whether or not your vehicle came equipped with an auto-tensioner).  With many serpentine belts, this can be difficult, as some pulleys will be hard to access with your hands, so be patient and make sure to seat the belt properly around each.  You will need to keep tension on the belt with your hands as you slide it into place to ensure it doesn't fall off while you're looping it around pulleys. If your vehicle has a belt only for the alternator, you will need to only slide it around the crank pulley at the bottom of the engine. If your vehicle is equipped with an auto-tensioner, use a breaker bar or appropriately sized ratchet to lower the auto-tensioner pulley last.  With the belt around all of the other pulleys, slide it over the tensioner pulley with pressure still on the breaker bar or wrench.  Once the belt is in place, slowly reduce the pressure on the wrench, allowing the tensioner pulley to tighten the belt.  Do not simply release the auto-tensioner, as that could damage the belt and cause injury.  Instead, reduce the pressure you place on it slowly. Remove the wrench or breaker bar from the tensioner pulley once this is done. If you loosened the alternator to remove the old belt, reverse that process by sliding the belt back over the alternator pulley.  Again, take care not to place too much pressure on the loosened bolts of the alternator.  If the belt is too taught to slide it over the pulley, loosen the bolts a bit more to allow the alternator to tip forward further.  Try not to remove the bolts to the alternator completely, as they will be difficult to reinstall under the pressure of the belt. Make sure the belt seats on the alternator pulley completely. With the serpentine or alternator belt safely seated on the alternator pulley, use the same wrench you used to loosen to the bolts to tighten them again.  As you tighten the bolts, the alternator will stop tipping forward, which will increase the tension on the belt.  Don't tighten one bolt completely before moving to the next one.  Instead tighten one halfway, then the other, before coming back to the first. If the belt seems to be putting too much pressure on the alternator, check again to make sure you have it run through all the other pulleys properly. Once you have released the auto-tensioner or tightened the alternator bolts, check the tension of the belt to make sure it has seated properly on all pulleys.  Pinch the belt between your thumb and index finger and try to wiggle it.  There should be very little give to a properly installed alternator or serpentine belt.  You can purchase belt tension testers at many auto parts stores that will tell you for certain that the tension in your belt is sufficient. If the belt feels loose, check to make sure it has been run through all of the necessary pulleys properly. Once the belt is securely in place, slide the ground cable back onto the negative terminal on the battery.  Use the same wrench you used to remove it to tighten the bolt, then wiggle the connection with your fingers to ensure it is not loose.  Make sure the ground cable is tight and won't come off while driving. A loose or disconnected ground cable could cause the engine to die.
Compare the lengths of the new and old belts. Run the new belt through most of the pulleys. Loosen the auto-tensioner and slide the new belt on. Slide the belt over the alternator pulley. Tighten the alternator bolts. Check the belt tension. Reconnect the battery.