There are many methods available these days, some more scrupulous than others!
One quick and easy way to dramatically increase the number of likes you have on Soundcloud, is to simply buy them! This is typically done by using a paid service, often in a country such as India where the people carrying out the service can do the work for comparitively low cost. They will typically get you around £1k likes for small charge of around £5 UK Sterling. The rationale behind this method, is that when genuine people visit your page, the more likes you have, the more they themselves are likely to 'Like' your tracks and profile - basically it's based on the premise that people like to follow what other people do, and if you already have lots of likes, people presume your music must be pretty decent to have warranted those likes in the first place.
The alternative couldn't be more different - as it basically involves lots of time, effort and resources in order to consistently build up the number of likes that your music obtains.
There are a number of promotional tools at your disposal, from posting links to your Soundcloud tracks on Facebook and Twitter and specifically requesting that people Like your music on Soundcloud, to handing out business cards to relevant people that you meet with a link to your Soundcloud account, and asking them to Like your tracks when they visit your Soundcloud page.
It's often a good idea to ensure that you specifically ask people to Like your tracks though - research has shown that they are much more likely to if you ask them directly!
Bascially, if you want genuine likes, there's no quick and easy way to obtain them - it's down to hard draft over many months and years to get people directed to your Soundcloud page and hopefully when they are there, a significant proportion of them wll like your music.
Just keep at it, and make sure you are persistant and use any suitable opportunity to tell the world all about your Soundcloud page and get them to go there and listen to your music. Good luck!