Choose an appropriate material. Use solid lumber or plywood for a basic wall case, metal for more secure storage and vinyl, plastic or glass for a case with views from all sides. Buy furniture grade lumber, oak, maple, walnut or similar woods for most household cases, and cedar, redwood or pine for southwestern or more rustic décor. Match the material to the purpose of the case, such as metal for tools.
Build a basic box of the size you need for your objects. Make a back first and frame it with top and bottom and side panels. Miter corners with a table or similar saw, depending on the material. Use a tape measure to get pieces to the correct size; cut corresponding elements, such as two sides, at the same time to insure they match..
Assemble the box with nails, screws or adhesive, depending on the material. Use glue or other adhesive to secure corners and the back. Countersink heads on wood cases so holes can be smoothed with wood filler or wooden plugs. Use a tack hammer or screw gun to install fasteners, with a nail set or countersink drill bit. Make corners square using a speed square to align pieces.
Decide how to mount the box; this will vary with the style and weight of the case. Cut out wall covering to expose studs to set a box inside a wall and fasten it through the sides to studs. Fasten the case back to studs with screws as an alternative. Use hidden mounting to conceal the screws by extending the back above and below the frame, installing screws in those elements and then concealing them with face trim on the outside of the box.
Make a door with molding or case components routed with a lip to hold a glass pane. Have glass cut to the exact dimensions of the door and secure the glass with brads driven into wooden framing or with a strong construction adhesive. Attach a door with decorative hinges and a latch, matched to the style of the case. Leave the front partly open but protect contents from falling with decorative vertical trim strips on the outside of the box.
Put shelves inside the case. Mount them with fasteners through the outside edges of the frame, with holes drilled to hold metal hangers or with cleats fastened to the walls to support a shelf. Make fixed shelves for permanent displays, adjustable shelves for cases in which objects will be rearranged or varied.
Design a wall case around an existing element, such as an antique window with decorative molding and possibly stained or frosted glass panes to make a door. Make a box to fit the dimensions of the window, using complementary materials, such as thick lumber for a large single-pane window with heavy framing. Finish a wall case with stain, paint or other protective coating; aluminum or plastic wall cases will not need these treatments.