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Know if you have a threaded headset. Loosen the bolt on the top of the stem. Loosen the locknut with a wrench. Pull the handlebars out of the frame. Wipe down and grease the stem lightly. Consider the kind of riding you'll be doing when deciding a new handlebar type. Place the stem back at your desired height and tighten the hex nut and top bolt.
Threaded headsets have one continuous metal piece (stem) that comes up out of the frame, bends forward, and then attaches to the handlebars. There is a nut where the stem leaves the frame that holds it in place and one bolt at the top of the stem. These stems are easy to adjust and are common on single-speed, fixed gear, and older bikes. Some bikes do not have a hex nut by the frame, and just have the bolt on the top of the stem. This bolt, pointing straight down, creates the pressure that holds the stem in place. Use an Allen key to loosen in, though your don't need to remove it entirely. Disengage the hex nut, which is the "ring" where the stem meets the bike frame, by loosening it with a wrench. You may need to wiggle, twist, and pull to get them out. If this is a new bike, mark the location where the handlebars used to rest with a marker or measurement so that you can return to this location if you need. Clean off any gunk on the stem with soapy water and then dry it with an old rag. To prevent the stem from getting stuck in the frame later on, apply a little anti-seize grease around the bottom 2-3 inches of the stem. Proper handlebar positioning largely depends on the type of bicycle you're using. That said, the number one concern when picking a height is rider comfort. You should put the handlebars where you can comfortably ride every time.  Road bike: Handlebars on racing bikes should be slightly lower than the seat to provide optimum aerodynamics and control at high speeds. Mountain bike: Mountain bike handlebars should be lower than the seat. This gives you a lower center of gravity and better balance when negotiating rugged terrain. Cruiser: Handlebars on standard bikes should be slightly higher than the seat to limit strain and provide maximum comfort. Hand tightness should be fine, especially with the top bolt. You don't want to crank on the bolt, making it so tight that you can't remove it later.