I found the installation instructions on the following SPM Wiki Page:
You will need to follow these steps to get SPM working:
1) Unzip spm12.zip in a folder of your choice, such as C:\Users\login\Documents\MATLAB\spm12).
2) Start MATLAB and add SPM into your path, either using File > Set Path > Add Folder... or typing the following in the MATLAB Command window:
>> addpath C:\Users\login\Documents\MATLAB\spm12
3) Launch SPM by using the command
However, please note that the SPM Wiki page has been marked as outdated. You might need to figure out some additional steps to get this working.