Carefully inspect the area where you plan on building your lean-to greenhouse. You'll need a standing wall strong enough and wide enough to fit the size of your greenhouse, but that's the least difficult requirement. The location of your greenhouse is of utmost importance.
Build your greenhouse against a wall that receives sufficient light throughout the day. Make sure the greenhouse will not be shadowed by the building you're building against or any other structures in the area. Build the greenhouse so that it is against a south-facing wall to best catch the sunlight. More sun means less heating necessary for your greenhouse. Use grow lights to provide artificial sunlight if you cannot build in a sunny area. Attach the greenhouse to a wall to provide you access to the electrical and water system inside your home, saving you the effort of having to run connections to a garage or fence placed lean-to.
Design adequate ventilation to your lean-to greenhouse. Because you must attach it to an already standing structure, you may be limited in your ventilation choices. Install a series of fans and vents to provide you with the necessary ventilation, though mechanical ventilation will raise the cost and energy consumption of your greenhouse.
Heating is another factor to consider if the sunlight does not provide adequate heat for your greenhouse. Install a heater or connect the greenhouse to an exterior window of your home, which can be opened to provide heat for the structure.
Construct your greenhouse out of easily obtained materials to help with any future repairs that might be needed. Build your frame using materials such as wood, PVC piping or aluminum. Use glass, plastic films or Plexiglas for the panels. Build your frame so that it is strong and stable enough to hold the panels. You'll also have to build the frame so that it can be adequately connected to your structure wall. Choose a panel material that allows the most light into the greenhouse possible without tearing or breaking due to the elements.
Design a lean-to greenhouse to include the flooring, the frame and the panels. Using plywood for the flooring is sufficient, and you can add a layer of foam insulation beneath, between the board and the ground for a bit more protection from escaping heat. Build the walls with a basic frame design, with braced studs leading from floor to the structure wall. Connect your frame securely with the existing structure, using the nails appropriate for your structure wall composition Use openings for your greenhouse that are as close to standard sizes as possible.
Maximize your available space by designing movable panels. Create hinged panels that connect to the frame and can be raised from the outside of the lean-to to access the plants. Although this creates an easily accessible design, it does have the disadvantage of allowing heat to escape whenever a panel is opened.