Help drawing a circuit diagram from a logic diagram
Converting a design "sketch" (which is really what you have drawn above) into a schematic involves three steps: finding real-world parts that match what you are trying to do, making modifications to the circuit based on the first step, and then drawing the schematic with some sort of schematic capture program.

For the last step, I am using the EAGLE program.  They have a free version that lets you create schematics limited to one sheet, like this one.

Here is the schematic I ended up with based on your drawing:



I just happened to have picked gates in the 74LSxx family; I could just have well used 74HCTxx (more suitable when interfacing with microcontrollers and other CMOS logic), or some other logic family.

Note that the four AND gates on the right side of the schematic are now actually NAND gates (74LS00 2-input and 74LS12 3-input), this is because I have configured the lamps to be driven low to turn them using a low output.  This is because the 74LSxx gates can sink about 8 mA of current, but can only source 0.4 mA.

We have to add an inverter after the 3-input NOR feeding the middle lamp since we can't easily turn it into an OR -- there is no 3-input OR in the regular 74LS00 family; they didn't bring one out until much later called the 74LS4075 which is not commonly available. (This where you have to make substitution based on what is really available.)

I didn't try to do any minimization of the logic and just converted the drawing as it is.  There are plenty of questions on this site regarding logic reduction.

Another optimization step that can be made, besides logic minimization, is to optimally use as many gates in a package as possible.  For example, there are six inverters in an 74LS04 package, and four NAND gates in a 74LS00 package.  If you need for example seven inverters in a circuit, and have an unused NAND gate, you can make an inverter out of a NAND gate by tying both inputs together.   There are scads of other tricks like this.

The resistors in series with the lamps are because the lamps are rated for 3v.  The resistors drop 2v across them at 8 mA.

On the left side of the schematic, I have the three switches.  They are also active low (when the switch is on, it grounds the resistor), so I have added an inverter at the output of each switch to make there outputs match your diagram.