1) Assemble the RGB LCD Shield per this tutorial
2) Assemble the DS1307 clock per this tutorial
3) Solder supplied male headers to Trinket
All components are hooked to 5 volts and ground. Note the ground pin used for the shield (the ground pin next to the 5 volt pin will NOT work, it isn't connected!)
Hookup of the display is easier with some male-female extension wires especially if the shield has male headers already soldered on. For breadboarding this allows the display to just plug in.
If an LCD display with I2C backpack were substituted for the shield, other data pins on Trinket could be used for buttons. Use of an I2C expander chip such as the MCP23008 or MCP23017 to gain an additional 8 or 16 pins respectively.
You can easily fit the parts for permanent mounting on a half perma-proto board, perhaps a quarter perma-proto board with some moving of parts. If you decide on a permanent mount, I suggest use of female header to mount the Trinket, perhaps even the clock module, in case the part has issues you can quickly swap it out.