Getting "big" in streaming is really hard to do, and most people will not succeed in making streaming a real income, but with the tips below you should at least be able to get a decent amount, once you put in the work required!
The tips are not really sorted in a particular order, so just read up on the ones that sound interesting, and try them out!
Trade hosting with peopleAfter all your stream, you should host other streamers, preferable ones that are about the same size as yours. Make sure you do some chatting in their channel, and perhaps even send them a message telling them that you like their stream. Hopefully they will follow you and also host you once they are done streaming in the future.
Another tactic is to make deals with some people where you actively host each other after each stream, sharing all your viewers with each other.
Create a websiteCreating a website for your stream can be a useful way to get your viewers more engaged, and even get them to share your content with their Facebook or Twitter followers. The website should be both a general info site for your stream, as well as a place where you post content. If you are streaming a MMORPG, you should use this website to post a few guides, give your opinions on content patches etc. to create some engagement with the community of the game. This will get your website talked about, and people will eventually use that website to find your stream.
Use YouTube to promote your streamEvery good streamer should have a YouTube channel where they post updates, guides, hightlights etc. Use this platform in two ways: 1) to keep your viewers updated even when they cannot watch your stream very frequently, and 2) to create content which attracts new viewers. Use the same strategy as above with the website to get new viewers into the videos and over to your stream. Make sure your Twitch name is very easily visible in the videos!
Stick to your scheduleA schedule is a very good way to keep your viewers coming back, because most people won't be able to watch at random times. Sticking to a schedule will make your stream look professional, and also make it easier for yourself to stream even when you are tired or not motivated.
Use Twitter to promote your streamMost people already use Twitter to tell their followers when they do live, but Twitter can also be a source of getting new viewers. The keyword is hashtags. Use these to talk about games, streaming and whatever is relevant to your stream, and with some luck you will be retweeted and noticed. Some streamers have been really lucky and got some retweets from game developers of the games they play on stream, which got them an enormous amount of viewers!
Twitter is also great for connecting with the viewers, so keep up the conversation there even when you are not live on your Twitch stream.
Apply for the Twitch Weekly SpotlightEvery Friday, Twitch has a stream which they talk about updates, the past week on Twitch etc. They also have dedicated some time to something called the Video Spotlight, which features streamers from pretty much all genres, and anyone who streams on Twitch can apply for being shown here.
In order to do so, you need to follow this link. Here you can upload the clip you want to share with everyone watching Twitch Weekly, and this is a very good method to get a lot of new viewers and followers.
The downside is that most of the people who apply for this gets rejected, since a lot of people apply compared to how many they can show, but it's definitely worth spending some time to prepare a really good submission for it.
Make sure your stream is of high qualityThis is not really a trick to get more viewers, but it is very important if you want them to become followers or stay in your channel. Make sure your internet connection is good enough, your PC is powerful enough, that your settings are correct, and that your mic is properly setup so it has a good quality. It's really important that the stream looks professional if you want to become popular, so spend a lot of time thinking about what you can improve.
If you need some external help, the subreddit called Stream Review can help you out. They will watch some of your streams and give honest feedback as to what is good and bad, and what on how you can improve it.