For the student in an English-speaking country wanting to learn Finnish, the only readily available textbook is Terttu Leney's TEACH YOURSELF FINNISH. However, inside of Finland a number of textbooks are written for the foreign immigrant market. Leila White's FROM START TO FINNISH, put out by the Helsinki firm Finn Lectura, is one such publication.
White's course expects no previous acquaintance with Finnish. She begins with a helpful list of things the speaker of English will find challenging (lots of endings, no articles). Grammar begins with the simplest of verb conjugation and noun declension, and even before that she tries to introduce individual phrases the student will find helpful in Finland (The text "Closed" on shop signs, for example). There's not much discussion of pronunciation, though she may assume that the reader has access to a Finnish speaker. White is clearly writing for the new immigrant to Finland as opposed to a linguaphile living in his home country. She gives a great number of slang terms one will encounter on the street, introduces Finnish customs (and tendencies to drink and carouse) with great humour, and explains the considerable differences between the written language and actual spoken Finnish.
Terttu Leney's TEACH YOURSELF FINNISH is, I think, the best book that the complete beginner should acquire. Nonetheless, White's book is a good place to turn next because, as the newcomer to Finland will soon realize, the literary language you learn Finnish must immediately be supplemented by the spoken form. White also has abundant exercises, allowing one to reinforce the material learnt from Leney's book.
I'd recommend using White as one half of an intermediate programme, using at the same time Leena Silfverberg's SUOMEN KIELEN ALKEISOPPIKIRJA and SUOMEN KIELEN JATKO-OPPIKIRJA for further training in written Finnish (both published by Finn Lectura). While it might be a bit of work ordering all these, and much in the latter two books is designed for classroom use, they will help you reach a level of comfort with the language when among native speakers.