I learned the basics from the introductory chapters of the book

• S. Albeverio, R. Høegh-Krohn, J. E. Fenstad, T. Lindstrøm, Nonstandard methods in stochastic analysis and mathematical physics. Pure and Applied Mathematics 122. Academic Press 1986. xii+514 pp.

The rest of the book is toward mathematical physics but the introduction is mathematically clean (using ultrafilters language), precise and useful. When I go back I always return to that book though I read parts of many others on the topic. There is a Russian translation as well (a translation is often a sign of an importance of the book).