To get used to hearing and producing the sounds of Russian, I suggest going through some videos on YouTube (Yandex, etc). Once you have a basic grasp of that and know some words/phrases, you can begin building your grammatical knowledge and vocabulary.
I'm using a number of paper resources—I'll be updating my bookshelf page to list these. Paper resources are especially helpful for studying Russian because they can be expected to be nicely typeset with accent marks for learners marked.
Currently, I'm making use of the following online resources:
Every dictionary/resource will have its own conventions for expressing stuff like case declension patterns nouns follow. Therefore, it is better to get well-versed with a couple of resources rather than jumping around and Googling stuff so that you can systematically build up a mental model of how this language is put together.
Additionally, I've been making use of Wiktionary for learning interesting etymological information about words I'm curious about.
Here are some practical observations and notes on what I've been doing with Russian.
Overall, the Cyrillic alphabet is really nice. Typing is much like in English—one keystroke gives you one letter. This is much nicer than doing all the finger gymnastics needed for typing languages like German or Spanish. If you've attempted Chinese, Japanese, Korean you will know the pain of Chinese Characters. None of that silliness with Russian. You can easily look up words by how they are spelled
Russian is a relatively homogenous language because of top-down planning by the Soviets, among other things. If you have some grammar question and know the proper terms to look up, you'll be able to find your answers in existing resources.
You must memorize lexical stress. Note that you have to do this more many languages, including English and German. It is kinda like memorizing tone for Chinese, except you only have to remember one thing (whereas for tone you'd have to remember the tone for every syllable of a word).
While Cyrllic is not so bad to learn, you will have to deal with some (1) spelling-pronunciation mismatches (e.g. the genitive masculine singular adjective ending -ого) and (2) some script variants—e.g. italic letter forms are different, you may have to read handwriting, you may encounter some now archaic letters.
Russian pronunciation is tough to get the hang of. There are many sounds in Russian that are not in other languages (linguists would call these sounds "marked").
There is a lot of "grammar" to memorize in the sense that you will need to learn many different forms for nouns (declensions) and verbs (conjugations).