In addition to all of the above advice, keep in mind the physics of hills as well. The formula for lifting an object up a certain amount of distance is p = mgH, where p is the potential energy needed, m is the mass of the object (you!), g is the gravitational constant and can be ignored for our example, and H is the height.

So basically the energy needed is directly proportional to the mass of the object being lifted. If you weigh twice as much as another rider, you need twice as much energy. So basically to climb a hill in X minutes, your power output will be Energy/Time, which is measured in watts. If you lower your gear ratio in half and take X*2 minutes, your power output will be cut in half. So what ends up happening is that a 150 pound rider can climb a hill in X minutes with ratio R by putting out power W. For a 300 pound rider, you will need to put out W*2 to take the same time, which isn't always realistic, and thus we need lower gears. For a 300 pound rider, a ratio of R/2 will take you X*2 minutes, but you'll still put out W watts.

Keep in mind that this is all roughly speaking. There's additional variables here such as the grade, wind, and tire resistance, but in general this rule is a good ballpark way to estimate how much gearing you need.

Now let's play around with BikeCalculator!

Bike Calculator
I weigh 420 pounds (ugh, I know). I know from experience that I can output 250 watts of power for an hour at maximum effort. So let's put those figures into the calculator.

For an 18% grade at 250 watts, I can average 1.47mph. Well that's just not realistic now is it.

Let's dive into more numbers though using Gear Calculator.

http://gear-calculator.com/
My bike has a 22/30 low gear. Input those numbers and set cadence to 70 (to prevent knee damage, you probably don't want to spin less than 70rpm under heavy load), and it says my lowest speed at 70rpm is going to be 4.0 mph. So like I thought above, climbing an extended hill at 18% is not going to be realistic. If I control for speed and alter the wattage, this tells me I need to put out slightly less than 700 watts to climb an 18% grade. Not unrealistic, but I also don't think I could handle more than a minute of that.

For you, you'll need to work backwards. If you're new at cycling maybe assume your long term power is somewhere between 150-200. Enter those numbers and your weight into the bike calculator and see what your expected speed would be up an 18% climb. Then go to the gear calculator and lower the gearing until you find a gear that matches your speed. It sounds like you have a compact, so you probably can't lower the crank any further than 34. So you'll be looking at getting a bigger cassette (which unfortunately might involve a new derailleur if you go too big).

A 28 cog is the biggest you can go on a small-cage derailleur. Shimano makes 12-30's now for mid-cage derailleurs, and 11-32/11-34's for long-cage derailleurs. That's about as low as you can go on a road bike, 34/34, giving a 1:1 ratio.

One final tip: if you attempt the hill but feel yourself in trouble, you can always do an impromptu switchback. IE: serpentine your way up the hill in S-curves. I would *ONLY* advise doing this if the hill is low-traffic. This move can be dangerous if cars whip by, especially since oncoming traffic sometimes can't see you (since they're coming over the top of the hill!). This method lowers the "effective" grade of the hill and will make it a little easier to climb.