Flat Design (& Android)"Flat" is currently a big design trend, with pretty much all the big players getting involved. One of the earliest big-hitters in the field was an iOS app called LetterPress (incidentally, the designer behind this has recently been working on Facebook's "Paper" app - which is also a pretty nice experience)
The trend found a surprising champion in Microsoft with their Windows Metro look (Windows 8, Windows mobile, xbox), before Apple(iOS 7) later joined the party as Jonny Ives took responsibility for software design as well as hardware. Now many of the most popular sites are sporting a flat look (Google flattened its logo, twitter went flat, even NerdAbility.com is sporting a flat design).
Flat design is about being more minimalist and user-focused - it skips the fanfare of effects or lifelike details for apps/backgrounds/controls and favours simple, clean, crisp minimal interfaces. It's kind of the opposite to the skeumorphic approach - which is using lifelike textures/look&feels for things (the obvious examples being on iOS pre-7 where the contacts have graphics in the background that make it look like a leather address book, or the notes app that has a lined paper background etc). It avoids fancy 3-d fonts and elements, avoids shading, shadowing, textures - and just uses simple colours, fonts, shapes to quickly convey meaning (see letterpress image above - no fancy rounded corners, fonts or textures - just simple block colours).
Flat Android DesignThere is no reason why you can't design an Android app following flat trend, in fact lots already have - Thankfully, as a core part of the flat trend is simple, it is simple to build flat looking apps in no time at all.
FontsThere isn't any hard and fast rule on fonts really - obviously it should be simple, clean and understandable - for this reason, clean, light san serif fonts have been a common font style to use. The most famous, as used by Microsoft, is Open-Sans - this is the font used across their Windows8 OS. It's popularity also boosted by the fact that it is freely available on Google Fonts, so has swept the web in a fairly big way.
Thankfully, as it happens, Android (since 3.0) has come with packaged with a lovely san-serif font called Roboto. The range of weights, especially the thin and bolder weights allow you to achieve similar aesthetics in line with common flat design, whilst presenting a professional, clean & simple typography. The obvious disadvantage of using the font is as it's built into later Androids, it's fairly widely used. Personally, I like to use it. I use the default Android font largely across my apps, and if I want to add a bit of character to a heading/title then I opt for the thinner version of the font.
ButtonsButtons are an interesting one. Whilst the flat trend is becoming more pervasive, there are still questions regarding buttons. Buttons have always been skeuomorphic by design - the shading and texture to show a raised/bevelled button (like a real life button that you might press) is classic skeumorphism, and whilst this is simple to switch to a 2-D, flat look&feel, there are still arguments as to whether you should do this - as the button look and feel communicates to the user that it is a button - it is so widely accepted a metaphor, people seem concerned that without the detail, people may not understand it is a button. How can they tell if something is a button or just a coloured block quote? (see this stackexchange question on the topic)
Above is an example from Windows 8 controls - as pointed out on the StackExchange link, all of those icons are actually buttons, along with the "Change PC Settings" - That could be fairly confusing, and would be an example of how not to design flat buttons.
Personally, I like flat buttons - as long as you take care to design the page so that the buttons are clear, and the form/page obeys general good UI heirarchy - an example of a simple form I was creating for an app with simple flat buttons is below:
As you can see, designing forms/controls that obey standard UI heirarchy and normal metaphors then it is still incredibly simple and clear what are buttons are what aren't. (I know it doesn't look like a fancy form - there are other decorations elsewhere as well though!)
ColoursThere are of course, no rules about colour - but there are trends. A simple google image search for flat colours will give you lots of palettes, and there are also lots of great free tools on the web for building palettes
Adobe's Kuler being a great example (lets you build schemes as well as share them with the community and look at other schemes)