Mobile home exterior doors are made like a sandwich with a metal or vinyl sheet on the outside, a Styrofoam core and a metal or vinyl sheet on the inside. They are manufactured to meet the minimum HUD codes and no more. That means they will seal tightly when closed and keep the weather out. It does NOT mean they will do much for home security. Aluminum, vinyl sheet & styrofoam is not a good foundation for crafting a secure door.
Manufactured home doors are sized by what the industry calls hole size. By that they mean that if you take the door out, what are the dimensions of the hole. You need to know these dimensions and whether you want the hinges on the left or the right before you go to buy your new door. You will also have to make some choices about what kind of window, if any, you want. Pick up a roll of putty tape and some extra screws at the same time you buy the door.
Replacing a door is generally not difficult, but check for obstructions before you begin. Sometimes decks are built high enough they cover the screws on the bottom of the door. If that is the case you may have some major work involved in getting access to them. The putty tape will stick and compress better if it is reasonably warm. A reversible drill with hex head bits is very helpful (almost essential). Buy the replacement door, putty tape and some new screws. Remove all the old screws, carefully pry the door from the opening and clean off the old putty and/or caulking. I say carefully because if you try to muscle it loose it is VERY easy to tear siding loose along with the door.
The biggest problem in purchasing a replacement door is proper sizing. This is one reason that most parts places won't ship doors. Even experienced installers will frequently buy the wrong size of door and have to return them once (or twice) before getting it right. Door sizing is a good place to have a conversation with your supplier. There are many options and issues that complicate matters. You can purchase mobile home doors or house-type doors, which have different sizing requirements. House-type doors can come with a pre-hung frame, which is quite different from the supports on a mobile home door. An important measurement is "hole size", which refers to the actual dimensions of the hole that the door assembly is installed in, rather than the size of the door itself (which is smaller). The following instructions refer to mobile home doors and not house-type doors.
Putty tape the new door, peel off the paper backing and shove the door into position. DO NOT loosen the screws that hold the new door in it's frame. These are what provide the strength to keep the door frame squared. The directions that may have come with the door will probably tell you to put three screws in at waist level on each side of the door and then work your way up and down. Before you get too many screws driven, check to make sure you have the new door in straight. (Maybe a level across the top would be a good idea?). Be careful not to drive the screws too deep. Power drills are strong enough that you can easily dent the aluminum door frame.
The door may or may not have come pre-drilled for a deadbolt lock. If not, you can buy drill bits that cut the right size holes, but I question the value of heavy locks for mobile home security. A heavy deadbolt lock may give you a feeling of security, but the reality is that for a determined intruder, a pry bar or even a hard kick is going to break through the door itself, no matter how strong the deadbolt. You need enough lock to keep out kids and casual entry attempts and show visible damage for filing a police report. More serious locks just make more expensive repairs and will not stop a real break-in attempt.