The Arduino team does not publish native Android versions of the Arduino IDE. Fortunately Anton Smirnov has come to the rescue with his program ArduinoDroid. It is available from the Google Play app store (free ad-supported, ad-free is $2.99). Load the program and you will have an icon in your all apps listing.
For this part of the tutorial, I will be using a Google/Asus Nexus 7 (2013 version) which has a 7 inch screen and weighs 0.64 pounds. It has dual band wifi 802.11 a/b/g/n, Bluetooth 4.0, and near field (NFC). The base model has 16GB flash and 2GB RAM. It has a microUSB port with OTG (on the go) main and secondary capability. There are a great variety of Android devices using various versions of the Android operating system. Other devices might not be compatible with OTG USB ports or the ArduinoDroid program.
You will need a microUSB male OTG to A female cable available from Adafruit and mobile shops at a reasonable price. This will provide you a full A male connection to plug in a cable to fit your microcontroller. For our Uno example, a standard USB A to B cable (Adafruit sells long and easy to pack short versions).
You may want to power the Uno from a separate power supply - if you use USB power, it will shorten your tablet battery life depending on the current draw and could exceed the power that can be drawn if you connect shields or other devices.
The program does not look like the typical Arduino IDE. It is a blank canvas with line numbering. If you turn the tablet in portrait mode, you can have the IDE and keyboard visible at the same time. You use the ... icon in the upper right to select what to do: load a file, or other actions you would do with the Arduino IDE menu bar. If you navigate to Sketch then Examples, you can go to 01. Basics and select the Blink example sketch.
You can download your own code via USB (like a flash drive), via Google Drive to a local folder or by cut and paste from a browser. The program is also designed to work with Dropbox (an additional fee may apply). You can select Sketch, then Open and you can select a recent sketch from the device or from Dropbox. Likewise Sketch -> Save as will save to the tablet local folders or to Dropbox.
The text is color-coded and is edited like any text file.
You can upload your sketch to the Uno by getting the menu using the ... icon, then Actions then you can Verify/Compile. Once it compiles cleanly use the same menu to select upload. I initially had an upload error but the code loaded. Subsequent uploads worked fine.
As of this tutorial's release, ArduinoDroid lacks a method or sending the program via Bluetooth although the author is considering it.
However, once you have your Arduino programmed, there are a wide variety of programs that can initiate Bluetooth communication with an Arduino connected to an Adafruit Bluefruit EZ-Link or Shield. Look in the Google Play app store, search for the term "arduino".