Most of the missions display professional models of their mission in the mission gift shop and examples of models built by others as displays in the mission museum. The San Gabriel Mission has large models of all the missions on display. They were built by seminarians in 1930s.
You asked for some ideas and help in building a mission model in a shoebox, which is a pretty small space. Most of the models we have seen are built on a larger platform but if that is what the teacher has specified you can build a small model that would fit. You will not have enough space to build the entire mission complex so you will probably want to focus on the church.
The San Juan Capistrano Great Stone Church collapsed in 1812 in an earthquake but there is an artist recreation of what it looked like on our website at www.missionscalifornia.com in the Galleries section. To save you time I am posting a copy here.
To start your mission project you should cut out a piece of heavy cardboard or even better, have your mom or dad help you cut a piece of plywood that will fit inside the shoebox, so you have a firm foundation on which to work. You will find it easier to build the model on a separate base that is open to work on, then you can place the finished product inside the box after it is done..
There is a book Projects and Layouts by Kari Carnell and Libby Nelson that describes how to build a mission, describes materials you can use etc. You can also find some a lot of instructions on the Internet.
You will find that models can be made of sugar cubes, styrofoam. paper mache or almost anything. You start by drawing the lines for the church walls, fountains, walkways etc. on the base. You probably want to leave room for a path or steps leading to the church. When you get to the roof you can cut out and bend cardboard in the shape of the roof, and then add ‘roof tile’ by gluing elbow macaroni or rigatoni pasta to the top and painting it brown or redish brown.