You can look at the assimp docs here: http://assimp.sourceforge.net/lib_html/data.html and http://assimp.sourceforge.net/lib_html/structai_scene.html
An asset loaded by assimp is assembled into several data structures. At the top there is the aiScene, which contains both a list of aiMesh mesh data, and an aiNode hierarchy for placing instances of the mesh data using various transforms and parenting. The scene also has a list of all materials and textures.
First you will probably want to create textures and possibly shaders from the list of textures and materials in the scene. The aiMesh data has all of the vertex data you need, so you'll want to create a vertex buffer for each mesh. Each mesh has one material, and each material can have multiple textures (color map, normal map, specular map, etc).
Then you walk the aiNode tree, calculate and set the transform, and draw the mesh referenced by the node. To draw the mesh, bind the shader and textures for the material used by the mesh, and then draw the vertex buffer.
If you want to support animation, you can look at the aiAnimation list in the scene. Each animation consists of a number of channels, which can affect a node's transform matrix. Skeletal animation is done via bone weights for the vertices of a mesh, and is a bit too complicated for this post.
I've written a simple opengl asset viewer based on assimp using the C api, which does skeletal animation. You can look at as an example: https://github.com/ccxvii/asstools/blob/master/assview.c