After training, testing and evaluating the model you have weight matrix (W) and bias vector (b). You can do prediction by equation below:

a=f(Wp+b)

a is the output vector and p is input matrix. 

I don't know what coding languages do you use. If you use Matlab, I suppose that you can use the neural networks toolbox in Matlab software. If you use Python, I think scikit-learn lib is the best choice for your research about machine learning. In addition,  there are tons of tutorials about machine learning and neural networks, you can search them by Google.

@Aliyeh & Pengbo Thanks

I am using Matlab.

Must tutorials I see are mainly on classification and recognition.

Like Aliyeh Kazemi have spoken. You can write a equation output = f(weight*input + bias) if your model have layer

If you use version Matlab 2013b or newer, you can use syntax genFunction(net,pathname) generates a complete stand-alone MATLAB® function for simulating a neural network including all settings, weight and bias values, module functions, and calculations in one file. The result is a standalone MATLAB function file. You can also use this function with MATLAB Compiler™ and MATLAB Coder™ tools.

I recommend you to go through the following article which discusses ANN training using PSO for solving regression and classification problems.

https://www.researchgate.net/publication/305325563_Codes_in_MATLAB_for_Training_Artificial_Neural_Network_using_Particle_Swarm_Optimization

Code Codes in MATLAB for Training Artificial Neural Network using...

Kindly refer

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