I want to build a website/mobile app for my school that shows the direction between two points similar to Google's directions API, but not with Google maps. I've got map shapefiles and GPS coordinates of buildings in the school and some programming knowledge (javascript, php, mysql), Please how do i go about it, I'm quite new to GIS programming.
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This is a challenging problem to start with! A good place to start is this tutorial on pgRouting, an extension to the PostgreSQL database with PostGIS, from one of our moderators. She has other posts on the topic here.
Once you have pgRouting working (no small task!) then you might want to check out GeoServer and OpenLayers for building a web-based interface. On your way feel free to post questions back to this site for help.