It is unclear to me how to change the locks on my front door. The handleset is old and the alignment of the deadbolt/key/knob doesn't seem to match what I see in Home Depot (see picture). Any advice on how to replace the handleset (or just the lock) without replacing the entire door?
This is a mortise lockset, meaning the lock mechanism installs into a pocket (mortise) cut into the edge of the door. Sizes on these can be a bit inconsistent, so if you really want to replace it (eg, to get a deadlatching spring latch, which I can't tell from the photo if this model has) you'll need good measurements, possibly several tries, and possibly a decorative plate to hide the fact that you had to drill new holes.
- Remove the cover plate from the door edge. It's held on by screws top and bottom.
- Looking into the now-exposed mechanism, you will see a setscrew level with the center of the lock cylinder. Loosen that setscrew a turn or two. It will then be possible to rotate the lock cylinder counterclockwise to unscrew it from the lock body.
- If there is a lock cylinder or thumbturn on the inside of the door, it probably mounts the same way the external cylinder did; loosen the setscrew and rotate the body counterclockwise until it comes free.
- Remove the thumb latch from the outside of the door, usually by removing the whole handle plate.
- Remove the knob from the inside of the door, along with the shaft that connects these.
- Now that you have nothing protruding from the mortise lock body, you can remove the two screws holding it in place (again, top and bottom) and slide it out of the door.
(Re)Installation reverses this sequence of operations. There may be some fiddly adjustment needed to get everything to line up. BE SURE to tighten the setscrew holding the cylinder until it bottoms out tightly in the notch in the cylinder's side; this is what keeps others from removing the cylinder to try to bypass your lock.
NOTE: If you just want this rekeyed rather than replacing the whole mechanism, go through the first few steps until you have the cylinder unscrewed from the lock body. Take the cylinder to a locksmith and ask to have it rekeyed or for them to give you a replacement, whichever is appropriate. Note that the exact details of the existing cylinder -- its length, what tailpiece it was fitted with -- may be important, so if buying an off-the-shelf mortise cylinder you need to make sure it matches these and/or make sure that you can transplant the tailpiece to the new cylinder (which is part of why I suggest going to a locksmith rather than a big box store).
Or ask a locksmith to do a site visit. This is a quick and easy job, but if they do it on site you'll have to pay the travel fee.