I have read both Serre's section on p-adic numbers in his book on arithmetic and Hartshorne's section on formal schemes; These both give a nice overview of some of the basic theory. In addition, I am familiar with some basic deformation theory, so I am happy deforming arithmetic surfaces to get curves over $\mathbb{Z}_p$ or $\mathbb{Q}_p$.
Where can I learn more about the use of p-adic methods for studying arithmetic schemes assuming this is the breadth of my knowledge?