That's already more of a schematic but it's not all. (A drawing like this is already fine, better a hand drawing then a Fritzing). A real schematic is easier to read to see what's wrong. A Fritzing is only useful to just build it wthout understanding. But if you have trouble building something from a schematic, just add pin numbers to the schematic (and maybe a drawing of the pin number on a component).
Alright, three parts. The first is driving the relay. The link is dead (Rapid is down...) but I found a datasheet. Although the relay is 5V the Arduino also has a maximum of current it can deliver. That's max 40mA and the relay draws in normal state already 71mA! That's not even counting the inrush current. So you have to use a driver for the relay like a transistor. Like so:
Second, like in that drawing, every coil needs a diode over it to protect the rest of the circuit from the fly-back voltage spike. A 1N4148 is great for that.
Third, like already mentioned by weedpharma, configure it in a way that one relay turn the solenoid on and the other for the direction.
But after reading all this, I would say, grab a simple motor driver and be done with it 