If you're developing a 2D game, and you know Java, go with Libgdx. It's great: very easy to use, cross-platform (Android, PC, and apparently iOS these days), and it also supports custom GL shaders if you want to do some advanced graphics programming.
For all non-game applications, assuming you know basic HTML/CSS/JavaScript, check out PhoneGap (or PhoneGap Build, if you want a simpler but $10/month approach to doing the same thing). PhoneGap takes your HTML5 app and packages it into a native application for Android and/or iOS. It's great for most fairly-simple applications, but I'm not sure it'd work very well for anything too graphically intensive, as I built a small game prototype a few weeks ago with it and it ran just a little too slowly. For anything other than games, I think it'd be a great choice.
Also, if you go the HTML5 route, Kendo UI Core is a nice web framework that makes your apps look native for each platform. In other words, when you compile your app for Android, it'll look like an Android app, while the iOS binary will look like an iOS app. I haven't tried it myself, but I've heard good things.
I went to a conference a couple of months ago where a guy gave a talk about using Kendo UI and PhoneGap together. Here's a YouTube video he uploaded of his entire talk: https://www.youtube.com/watch?v=j8L1fLVgYPA
Lastly, you didn't mention which platform(s) you're intending on targeting, but if you're undecided, you might want to start with Android. iOS has a much higher barrier to entry. While Android's Play Store has a one-time fee of $25 for a developer license, iOS requires an annual $99 fee for its license.