Actually, broadening/improving one's language skills is a very broad concept, it should be done in more than one ways at the same time which is highly recommended. One can NOT become better ONLY in one area e.g. speaking, one MUST improve skills in ALL dimensions of the language!
Learning language well requires being as active as possible and making the learning as FUN for oneself as possible. Taking lessons is always important, but equally important are these:
1) Listen/watch: Keep listening to internet radio stations like BBC, watch TV shows in English (use only subtitles, NOT voice dubbing in case you are not a native English speaker!), etc.
2) Write/communicate: Try to find discussion forums from the web about things that you find interesting (music/various artists, hobbies, etc.) and start communicating there with other people using only English. Start using instant messaging systems in case you find some new friends or start emailing them.
3) Buy yourself a proper dictionary, and each time when you see a strange word that you do not understand, look it up. Putting words into their CONTEXT is one of the best ways to broaden one's vocabulary and grammar knowledge, the more you read and write the better. Memorising is NOT the best way to go with learning grammar or any other language areas!
The main point in ANY language learning is to make it as fun as possible for yourself. Try to find topics that INTEREST you, read online newspapers (Times, Guardian, Independent...), listen to BBC/NBC and other radio stations online, if you find a discussion forum for e.g. your favourite hobby or your idols in music do participate there, etc. The key word here is CONTEXT, which means that it is easier to learn new words and their usage as well as grammar when you use/see them in their real CONTEXT. The more you see and hear the new words in their context and the more you use them in your speech & writing, the easier it becomes to remember their meanings.
I'm sorry there is no easy way out with this, one really must develop language skills in ALL these language "levels" or dimensions in order to reach better language skills!!
As for conversational skills, only practice makes perfect. Don't be afraid of doing mistakes because even native speakers do them! The nonverbal communication is indeed very important part of communication, but it improves along the way if you are as natural as possible.
Last but not least: NEVER EVER use ANY online translators, they are nothing but utter rubbish!! English is practically EVERYWHERE in the online world these days, you just have to use your imagination to find it! Learning pace is always personal, it takes the time it takes so there is no reason to hurry it up too much. If you do, you will not learn so well. Also, please learn the basics of the standard English first before advancing to finer details like dialects/accents.