Remembering the rules of Russian grammar is a daunting, and time consuming chore; but, it is very well worth the effort.

Two quick things:

1) I suggest buying the Big Silver Book of Russian Verbs - it will help you learn which verb requires which case. Not all verbs take accusative. For example, the verb 'звонить' takes dative: "Я звоню моему брату каждый день." With the verb 'to find' you do use the accusative however.

2) Remember that adjectives will ALWAYS decline to match the noun they are describing in gender, case, and number. If it helps to remember, find your verb and which case it requires, decline the noun, and then decline the adjective to match the noun.

Найти - to find, with an direct object (Accusative-noun)
Книга - declines into the accusative
Эта - the adjective 'this', describing 'book' - so this must decline into the accusative as well to match the noun.

I hope that all makes sense and helps (Comprehensive Russian Grammar by Terrance Wade is a fantastic book, and has a workbook you can buy to go with it. I'm currently working with it, and highly recommend it).