Dictionaries

Большой толковый словарь русского языка. 

Толковый словарь Ожегова.

These dictionaries give you a precise definition of a word in Russian. Often you will also find example sentences, collocations and idioms.

ABBY Lingvo

This is the most popular online dictionary which allows to translate into Russian from 20 different languages including English, German, French, Chinese, etc. Besides, it provides multiple example sentences, word forms, and pronunciation. Also, you can look up inflected forms which is very helpful when you are not yet familiar with all the various word forms.

Multitran

It is an online dictionary which is constantly updated by users. There you can find translations which you won't be able to find anywhere else. But beware, not all the users are linguists, so their translations are not always precise.

Corpus

Russian National Corpus

In addition, you might find very useful Russian National Corpus. It is a reference system based on a collection of Russian texts in electronic form which contains more than 500 million words. It can help you understand how to use an unknown word in any grammatical form.

Grammar

Learn Russian

As for grammar, in my opinion, the most useful and intelligible explanations are offered on the site Learn Russian by Russia Today. It also helps you expand your vocabulary and learn basics of Russian phonetics. Besides, you will find there convenient grammar tables.