This project is fairly simple for someone well versed in microcontroller programming. Without a microcontroller it would be a quite advanced project, needing on the order of 10 or more logic chips. In fact, I am not even sure how one would go about it without a microcontroller.
Basically, to dim LEDs you want to use PWM (Pulse Width Modulation), which means you turn the LEDs on and off say 100 times per second, the % of that time period that it is on determines how bright it looks. At 100 times per second, it does not look like it is blinking because they eye is not that fast. The % of time on is called the duty cycle. It can go from 0% (off) to 100% (fully on).
In addition to doing the dimming, the microcontroller would have to monitor the buttons and respond to them. For an experienced programmer, this is easy, for someone who has done no programming or electronics it would be quite a learning curve.
If you want to pursue this, people will help you here on the forum, but don't expect it to be a weekend project!
Bob