Lykke is not a big platform (yet) but I think it is working quite well. The founder is a co-founder of the well known FX platform Oanda. To me this and the fact how they handle things shows this is a serious project and it is safe to put your money in. I have bought a few times through their platform and though fees are a bit higher it works very well.
You can start by downloading the app from either the Google Play store or the App Store for iPhone. You can find both on their website.
Again, we will run you through the sign up process below so you can start buying.