I'm not sure how to put this without sounding negative, but I don't think its as easy as just toss a bunch of components into a shopping cart and then go build this from this schematics. Well ok it kind of is, but not if you don't know what the components are or does. Seems this schematics leaves some experimenting to be done. On the other hand, it can be a great way to learn 
But - it would help if you would clarify what you want to do. I would guess a light-following robotic arm (but what kind of light? The sun? A flashlight?) And how you want to finish it, a PCB, stripboard, just the protoboard, something else..?
Plus the schematics leaves some details out, like:
- how to (physically) arrange the photo diodes (im guessing thats what it is - yeah I don't know what everything is myself). For a light following something, they would need to be fastened to the moving part.
- what kind of photo diode? (It's not a solar cell, but I guess solar cells would work too - but then you'd need to adjust the feedback resistor I guess, or maybe you wouldn't need the opamps at all with solar cells(experiment)).
- and more..
Also I'm not so sure about these op-amp circuits either, even if they might work for the author of those. What's the point of the 10k resistor from the op-amp output to ground for instance? Of course it could be my limited understanding of op-amps, but to me it just looks like an unnecessary load. And probably erroneously though to be amplification ratio (Rfeedback/Rimpedance...ish..but I'm only guessing here!) Amplification seems to be depending on the internal resistance of the (unknown) photo diodes. Who's to say you got the same type?
As far as I can see they use a dual voltage source (+V, -V, and ground). That is also something to consider if connecting these to an Arduino analog inputs. Of course you could "fake" a ground at V/2 with a simple voltage divider and yet another op-amp.
And also at least one minor error: It says "Pin 6" (presumably a pin from the Arduino) on the "switches" schematics (MovDnSw) are also on the "Rotate relays and motor drive" schematics (RotLeftDrv). No biggie though, just use another pin.
Like Dilbert98122 says, since you are using an Arduino, I don't see the point of using the swithces circuit at all to prevent you from pushing both up/down or left/right simultaneously (unless you skip the arduino part and connect those directly to the relays schematics). You can prevent that in software. Which you should anyway, as the relays schematics are shortcuts waiting to happen if left/right or up/down are activated simultaneously.
In fact when I think about it, better use of the swithces schematics would be on the output from the Arduino, to be on the safe side (If you want to do it with relays like that).
Apart from the OWI 535 robotic arm which I don't know anything about, I don't really se any very special components here. Maybe the 5V SPST relay. A quick google on "5V DIL SPST relay" or similar should provide some results.
Otherwise just resistors, capacitors, diodes, transistors, some logic circuits, LEDs and op-amps..
As an example, the MC34071 is an opamp. LM741 another.. there are hundreds if not thousands to choose from. And I'm not sure if the op-amps needed for the photo-diode (if that is what it is), needs to be of a special kind or not (probably not).
74HC02 is a quad 2-input NOR gates in a DIL package. 74 Series Logic ICs
There's also the 4000 (CMOS) series to choose from.. 4000 series CMOS Logic ICs
4001 is yet another quad NOR gate.
Now slightly off-topic:
As for asking people to help you via email I think is really misunderstanding the point of a forum. Not to mention pretty "demanding" of people (Sorry I don't know how else to put this in good english). You can't really expect people to work for you like that (unless the pay is good :P).
Also, no-one would be able to search and find a possible solution to something similar in the future.
Plus, like Mike says, the more eyes the better!
ok rant off 