It looks like you have the contrast pin (3) connected to ground. If that gives you good contrast, stick with it and you can forget the 10k ohm pot - makes life simpler!
For the backlight, you can use a 1k (1000 ohm, or use 250 ohms if you can get it) pot with switch (same style as you have for the 10k pot I think) to allow brightness control and be able to switch it off completely, all with one control. Note that the brightness control won't be very linear - most of the useful control range will be at one end of the pot rotation range. Some clever circuitry is needed to make a really smooth brightness control.
You can put the brightness pot on the ground side or the +5V side of the backlight LEDs - it doesn't make any difference to the performance. Most of the diagrams I've seen (including the LCD Smartie site) have the pot on the ground side so I'll stick with this method.
To wire your LCD as per caesar's diagram (like standard Smartie circuit):
Pin 1 to ground.
Pin 2 to +5V
Pin 3 to ground (if the contrast is OK like this)
Pins 4-14 to appropriate port pins
Pin 15 to +5V
Pin 16 to one end of 100R (100 ohm) ordinary fixed-value resistor
Other end of 100R resistor to middle pin of pot.
Pot's clockwise-end pin to ground.
What I mean by "clockwise end" is the pot terminal that has zero resistance to the middle terminal when the pot is rotated fully clockwise. That will give max backlight brightness when the pot is clockwise, and min brightness when counterclockwise (like a volume control). You can wire the pot's switch (if it has one) between the clockwise-end pin and ground to allow you to turn the backlight completely off.
Right, I hope I've explained that properly and that it makes some kind of sense!
PS: For the resistor values, "R" means ohms (eg 470R means 470 ohms, 2R2 means 2.2 ohms), "k" means kilo or 1000 (3k3 means 3300 ohms, 10k means 10000 ohms), "M" means mega or 1000000 (1M5 means 1500000 ohms). A similar system is used for capacitor and inductor values, but these are usually very small numbers with values in the nano ("n" = 0.000000001), micro ("u" = 0.000001) and milli ("m" = 0.001 - note lower case) range (eg "4u7" on a capacitor means 4.7 microfarads). Like any technical subject, electronics has heaps of jargon!!