First of all, the oscilator will do just that, oscilate. If you want the lights to have a constant on mode, build a switch into the circuit that is configured as shown below, which will switch power from the oscilating circuit to the LEDs directly. You can even get a potentiometer (the knob) that has a SPDT switch built in, thus the "knob" will click at the end of its turn cycle and will switch to solid mode.
Start your project by building a 555 timer to blink one LED as a fixed rate. You won't need a transistor to drive one LED, and you won't need any knobs. Then build on the project as you learn.
In my diagram, you see how you can switch from blinking to solid. D1 is any common switching diode, there are usually available at Radio Shack in bundles of 50 for only a few dollars. This is important here to keep the 555's CLK pin from being driven high when you switch to solid mode. R1 is a resistor that will lower the voltage that you are applying to the base of the transistor to less than the differential threshold to switch the transistor. This is important because if the voltage at the base and at the collector are the same, or the base is higher, the transistor will not let current flow from the collector to the emmiter (and you might let the smoke out too
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Hmm now that I look at it I think all the LEDs in my diagram are backwards, anyway just put them in so that their positives are connected to your power supply and the negatives to the transistor (or ground if you are building a circuit without the transistor).
Learn more about the 555 circuit and build a circuit with just a single blinking light. Then try replacing one of the resistors with a potentiometer (which is the "knob", it's a resistor whose resistance value is adjusted depending on how far the knob is turned). This will take some experimentation to get results that suit what you want. The 555 is an easy to find chip that you can get at Radio Shack. They also sell boxes of NPN transistors. (There are two types, NPN will allow current flow when there is voltage at the base, and PNP, which will stop current flow when there is a voltage at the base.)
After you figure out your 555 timer, build a circuit with many LEDs that you can drive with a transistor. If something smells funny, don't use that transistor again
. Once you get those two circuits working, just combine them! Allright, well, good luck!
P.S.
I left out the drop resistors in the digram too. For a plain old LED with a 9v supply, you will prolly need a resitor before each LED with a value of about 470 Ohm to 1KOhm. Again, this is dependant on the LED, just play with what gives you the birghtest LED output without getting the resistors real super hot.