The relationship is linear. Keep the shutter open for twice the time, get twice the light. This is known as "one stop", and you can use that in conjunction with your light meter to get the desired results.

The built-in light meter in DSLRs usually gives the value in stops — basically, the number of halvings-or-doublings from what the meter thinks is correct. (See What is one "stop"? for more on this concept.) So if it says "-1", simply double the exposure to bring it to 0. If it says -2, double twice (going from, say, ¹⁄₆₀th of a second to ¹⁄₁₅th). Or, the other way around, if the meter says you're overexposed by a stop, cut the shutter speed in half.

If you have a fancy external light meter, it may give you the option to fix the aperture and ISO and literally tell you what shutter speed to use. In that case, of course, do that.

You note in a comment above that you want to shoot manually rather than using aperture priority mode. There are plenty of good reasons for that, but whatever yours is, you might want to look at What is the relationship between ISO, aperture, and shutter speed? as you figure it out — answers to that question cover this and more.