classical conditioning paradigm for hippocampal learning
First of all, your first sentence assumes something which may not be true and is still controversial in the literature. Learning and memory are thought to be related to the phenomenon of LTP but it appears you are taking this as a given. 

There is a huge swath of literature on hippocampal-dependent behavioural tests like the Morris-water maze etc so I assume you are already aware of these. If you wish to monitor the HPC firing pattern: 
1) during training --- you can set-up an in-vivo electrophysiology platform coupled to a virtual navigation interface and record from cells while the animals are performing a spatial navigation task.
2) after training- you can take slices from the animals as is classically done and try to induce LTP and see if your spatial learning task has influenced the amount of LTP you can get. The condidtioned and unconditioned animals will simply be the two groups which you can compare to see if the behavioural readout(spatial memory task) corresponds to changes in what is though as the cellular basis for memory(LTP)


  Whitlock, J.R., Heynen, A.J., Shuler, M.G., and Bear, M.F. (2006). Learning Induces Long-Term Potentiation in the Hippocampus. Science 313, 1093–1097.
  
  Goh, J.J., and Manahan-Vaughan, D. (2013). Synaptic depression in the CA1 region of freely behaving mice is highly dependent on afferent stimulation parameters. Front Integr Neurosci 7.
  
  Heynen, A.J., and Bear, M.F. (2001). Long-Term Potentiation of Thalamocortical Transmission in the Adult Visual Cortex In Vivo. J. Neurosci. 21, 9801–9813.