Grove sensors without a Grove shield
From the wiki.
Above is a schematic of a Groove shield. You can see that each of the connectors has two digital pins connected to it and then V (5V) and G (GND). The last two you can connect normally to an Arduino. The first two you connect to the pins that are used in your sketch.
Say it says to connect the connector to the top left DIGITAL pin on the board (D6/D7). You'll 7want to connect the pins as followed: Black → GND, Red → 5V, White → D7, and Yellow → D6.

Notes:

The shield overlaps the pins (i.e. 3-4, 4-5), so that might make things confusing. I think that is a design flaw. If it needs two pins, it should have two connectors. In the current state, you can connect two things together. I don't really know how to figure out if it uses all of the ports attached or not. If you don't have to, I would try not to overlap any two grooves. You would do this by using two digital ports for every groove &quot;module.&quot;
You'll also need to have a adapter cable (Link from TheDoctor's Answer.)
For analog connections, it applies the same way as digital. G is ground, V is 5v, and A# is an analog pin.


Inferencing it:
There's no real cookie cutter way to connect to them. However, the wiki seems to be a decent resource once you figure out how to navigate it. The dust sensor you mentioned seems to ONLY use digital pin 8. It was connected to the D7/D8 connector on the Groove shield, so the yellow wire could be ignored since it was never used in the sketch.
It's hard to do much with this system: it's poorly documented and not uniform at all. Plus, some boards could cause problems that could even lead to damaging components. I would say look at something else.

This dust sensor seems pretty good, minus the documentation. On this blog, they say to do this:


Sharp pin 1 (V-LED)   =&gt; 5V (connected to 150ohm resister) Sharp pin 2
(LED-GND) =&gt; Arduino GND pin Sharp pin 3 (LED)     =&gt; Arduino pin 2
Sharp pin 4 (S-GND)   =&gt; Arduino GND pin Sharp pin 5 (Vo)      =&gt;
Arduino A0 pin Sharp pin 6 (Vcc)     =&gt; 5V

I can't seem to find the cord for it, but I'm sure there are many others like this online. (It lists the cable needed: a 6-pin, 1.5mm pitch connector. That doesn't seem too hard to find).

Here is a 4x7 segment display for much cheaper. It does use a lot of pins and need resistors, but multiplexing and resistors aren't that hard to figure out. That's outside of the scope of this question. There might be some other board with a built in IC for controlling a display like that, but I can't seem to find one now.