This handbook was written specifically for beginning students. It presents twenty-seven graded readings, each accompanied by a vocabulary and an explanation of grammatical details; the final chapter provides a sample of the Codex Argenteus. Among the readings, the first seven are in effect preliminary exercises. The remaining twenty readings represent the Gothic Bible and the Skeireins . The external history of the language is also outlined, as well as the elements of phonetics, and the essentials of phonologic and analogic change.
Because of its shared Germanic origins, Gothic can seem one of the most accessible ancient Indo-European languages for English speakers, but a good textbook helps. I found William H. Bennett's The Gothic Language: An Introduction the best way to get started with the language. I should note that I have an extensive background in comparative Indo-European linguistics in general, as well as a solid knowledge of Greek and Latin, which means I may have had an easier time with the book than might readers with less experience.
Bennett teaches the language from both a synchronic and diachronic perspective, the latter increasingly prominent as the book goes on. Each of the twenty-eight chapters follows the same format: a reading selection (artificial texts for the first several chapters, then real extract from the manuscripts) along with helpful footnotes and vocabulary, then an explanation of new noun or verb paradigms, and finally a description of how a particular feature of Gothic phonology evolved out of Proto-Indo-European. Exercises are presented to test one's knowledge of both synchronic paradigms and sound changes. All Gothic text is presented in the standard philological transliteration into the Latin alphabet; only in the last chapter does Bennett describe the Gothic alphabet and offer a facsimile of a manuscript page.
The main "competition" to this book is Thomas O. Lamdin's An Introduction to the Gothic Language, but I would really recommend buying both and reading Bennett's book first. Bennett is simpler, covering just the basic. Lambdin, however, goes into much further detail (word formation, historical development of morphology and syntax and not just phonology) and gives much longer reading passages, which might scare away those with no prior experience, but acts as an ideal intermediate/advanced text after Bennett's primer.
While I think this is the best way to get started with Gothic, there are some infelicities that could be solved in the next printing (the book has already gone through several editions in 1960-1980). Bennett stops giving exercises for paradigms fairly early in the book, and while you could always do your own paradigm drills, some lazy students benefit from the book forcing one to. Also, not all words used in the exercises are present in the glossary at the end of the book, which makes it hard to check one's exercises without the aid of a teacher or a Gothic dictionary. (If you take my advice and purchase Lambdin's book too, then its glossary will fill in many gaps).