It will be nice if some of us (Arduino rookies) can get the details of how to combine other hardware like the RTC and sensors with the LED modules we've built.
This is an interesting question and I think goes more to the way of thinking about hardware in the Arduino world than the hardware itself. Most of the simple modules used on these forums can be purchased cheaply and provide a few pins to interface to the Arduino hardware. By and large the interfaces are either Direct I/O or consist of ICs with bit-bashing serial interfaces (like the 595 or the MAX7219) or I2C or etc. The key here is that most newbies don't look at the datasheet for the hardware and jump right in, without too much understanding of what they are doing. Reading the datasheet (as difficult as some of them are!) at least gives a reason for why things are done as they are, and builds a knowledge of how to deal with classes of problems. An SPI interface to an IC is pretty much the same no matter what IC it is, so you just need to learn it once.
To take the example of the time and temperature displayed in the example video and sketch. The way I start these things is to build a knowledge of how the devices work (LED display, DS1307 Clock module, Temp sensor) individually. This requires some experimentation and code, independently of the final project device. This can be built up as part of general learning and experimentation (my preferred mode) or just specifically what is required for the project at hand. Google is a big friend here. In the software world this would be consistent with writing a function and a test harness to exercise the code to see 'what happens if ...'.
I use a 'sensor shield' arrangement and build small circuits for individual sensors on a 1"x1" prototype PCB. The sensor shield has standard Ground-Voltage-Signal (GVS) pins for each Arduino I/O and ready made 3-pin connectors can be bought in this configuration. This allows me to quickly combine the devices in different ways to test ideas. Many of the experimenter kits work in a similar fashion, but having to build the small test circuit forces me to read and understand the datasheet. I have described this arrangement much earlier in this thread, I think. [ Edit: Here it is LED matrix display - MD_Parola, MD_MAX72xx and MD_MAXPanel - Exhibition / Gallery - Arduino Forum].
Once over this hurdle, integrating the devices comes down to what the project is about, which becomes quite specific to the application. The sensor shield once again allows me to mock up a large part of the functionality required before I build the final circuit. I will also, at this stage, usually breadboard some of the circuit that is not standard or too large to fit on the small protoboards.
Hope this helps. My background is in software but by breaking down the hardware into manageable 'subroutines' the ideas behind what is going on become quite manageable and easier to understand and integrate.