Russian language has some of the most unpredictable stress patterns. Stress can fall on different syllables in different words (пра́вило, а́рмия, челове́к). It can shift from syllable to syllable within different forms of the same word (вода́ — во́ду, при́нял — приняла́). What complicates the matter is that stress can change the meaning of the word. Compare "за́мок" (castle) and "замо́к" (lock), "в ду́ше" (in the shower) "в душе́" (at heart).
Even native Russian speakers are prone to mistakes and ambiguities when deciding on where to put stress in certain words. For example some Russians say "кто-то звони́т" (somebody's calling) and others prefer to say "кто-то зво́нит". For this reason, there's not much choice but to memorize stress. Try to make a habit of consulting with a dictionary, asking a competent native speaker, or using special software that shows stress marks.
From my personal observations (which is not definitive) Russian speech tends to be stressed on syllables closer to the end (last but one or the last one). This is especially true for last names and totally different from English where words tend to be stressed on the first syllable.
An interesting feature of Russian stress is that not only words can be stressed but phrases as a whole too. The following phrases merge and and have only one stressed syllable: на́ слово (as in ве́рить на́ слово), не́ было, не на́до, etc.
As for specific patterns, there would be too many to remember. However, it might be beneficial to know at least a few of them:
the letter ё is always stressed (with rare exceptions of borrowed and complex words like трёхъя́русный)
the -ый and -ий endings are never stressed
the -ство and -ость endings are rarely stressed (коли́чество, де́тство, ра́дость, ли́чность)
words containing -тель- tend to have the preceding syllable stressed (зри́тель, чита́тель, пита́тельный)
words ending in -ие and -ия also tend to be stressed on the preceding syllable (чте́ние, зре́ние, посвяще́ние, исто́рия, компа́ния, револю́ция) with certain exceptions
words ending in -ак tend to be stressed on the last syllable (таба́к, дура́к, зодиа́к) with exceptions (за́втрак)
Note: Stressed vowels are marked with the acute accent ( ´ ) in Russian.