I normally shoot wide open around ƒ/2.8 or ƒ/4. Why? Because you need the added light from a large aperture opening, and chances are, depth of field isn't as critical. For my white balance, I prefer Incandescent. This white balance will turn the night sky into a purple pincushion of stars and looks great for the Milky Way.
Next, I'll turn on my camera's long-exposure noise reduction. My shutter speeds are going to be slow, so turning on long-exposure noise reduction in-camera greatly reduces noise over a long exposure. Note that enabling this feature will double your exposure time, so if you take a one-hour star-trail shot, your camera will process the shot for one hour after the shutter closes.
FOCUSINGThis is the crux of night photography, especially star trails without foreground. I always bring an inexpensive rechargeable flashlight with me on night shoots. Sometimes I use this for light painting, but other times I use this to shine on foreground subject matter to help me focus in the dark.
The first step with focusing at night is turning off your autofocus. Your camera autofocus won't work, and if your shutter is linked to focus priority, your camera won't shoot. I start by setting my focus to the infinity mark (the "figure 8" symbol located in the distance scale on your lens barrel). Line it up with the focus mark on your lens, and you've focused at infinity. But this may not be perfect focus. Infinity focus is a reference, but will slightly vary on the lens. I often focus to infinity, then back off just a tiny amount and take a shot. I'll review my image after capture on my LCD screen to check critical focus. If I'm off just a little, I'll slightly adjust the focus and try again.
If this sounds tedious, just think of it this way: Once you know where the accurate infinity focus is on your lens, memorize it. The next time you shoot at night, set your focus to that mark. I'll even attach a piece of gaffer's tape on my lens to hold the focus in place.
A new tool that many photographers like for focusing at night is the CamRanger. This device allows you to set your focus using an iPad (or iPhone). Viewing the larger screen is nice and dramatically helps with focus. You can tap anywhere on your iPad screen, and the camera will focus on this point. The CamRanger goes a lot further than just being a focus aid. It also allows you to adjust settings and remotely trigger your camera. Just imagine shooting that star-trail shot from the warm interior of your car!