Creating a basic feed forward perceptron neural network for multi-class classification

I am new to neural networks and I want to create a feed forward neural network for mutli-class classification. I am allowed to use any code that is publicly available but not any MATLAB ToolBox as i don't have access to it (so no neural network toolbox). The goal is to classify the data into one of 10 classes. Here is the data set, the class is defined by the three letter code in the last column.

When creating a neural network, do you simply define the amount of nodes and have each node in layer i connect to every single node in layer i+1? And then simply have them learn the weights themselves?

Also is there a source I could follow that has MATLAB code for creating a neural network with any amount of input, any number of nodes, and does multi-class classification that is feed forward.