There are several options.
You can do star trail photos with just a tripod. If you have dark skies, Point the camera near the pole star, do a long exposure, and get star trails as the sky appears to rotate around the pole.
If you're in a light polluted area, then you'll find your maximum exposure time is limited by the light pollution - expose for long enough and the light pollution background will saturate one or more colour channels - which could prevent you using a long enough exposure to get long trails.
You can also take pictures of the moon - since it's basically a gray rock in bright sunlight, you don't need a long exposure at all for this. But you do need a long focal length to make the moon big enough to fill a decent part of the frame, and at 150 mm it's likely to be disappointingly small. (You need around 1500mm or so to fill most of an APS sized sensor frame).
You can also do constellation photography with just a tripod. The trick here is to keep the exposure short enough that the rotation of the earth doesn't cause significant star trailing. As a rough rule of thumb, divide 400 by the lens focal length to get the approximate exposure time in seconds (thus varies in practice depending on where you're aiming, and how picky you are about trailing, but should give you a starting point). Thus with a 50mm lens, you can get away with around 8 seconds, around 2-3 seconds with a 150mm lens, and around 33 seconds with a 12mm lens.
You can improve results by stacking several exposures in software - try the free Deep Sky Stacker - which will reduce noise and usually give you a cleaner result.
For longer exposures, you'll need some sort of tracking mount to compensate for the earth's rotation and prevent star trailing. You can either build a barn door tracker, as mentioned in other replies, which rotate a camera platform around a hinge whose axis points at the celestial pole, or look at a commercial solution.
There are several mounts designed for use with cameras, such as Vixen's polarie, Skywatcher's star adventurer mount (or similar from Vixen or Ioptron), or the Astrotrak system (or Kenko's Sky Memo (not sure if this is still available)). Note that with some of these you also need to budget for a couple of tripod heads - one to point the mount at the celestial pole, and one to point the camera.
Or you could look at a motorised german equatiorial mount - which would also let you use a telescope - but to get good long exposure images with a telescope usually requires a good mount, which range from expensive to very expensive - and may also require autoguiding (automatic correction using a second guide camera and software) to apply corrections for long exposures. Long exposure deep sky imaging is more accessible than it was, but is still expensive to do well (and easily capable of soaking up as much money as you want to throw at it.)
Note that popular go-to alt-az mounted are limited for long exposure imaging, as although goto alt-az mounts can track objects - which is fine for visual use - they suffer from an effect called field rotation which makes the field of view gradually rotate, causing star trailing after a while (around 30s or so - it depends on latitude and where you're pointing). German equatorial mounts, with one axis pointed at the celestial pole, don't suffer from this.
For planetary imaging, the planets are bright enough that you can capture video with a webcam (or similar planetary astro camera) and telescope, and then process the video to stack the best frames. This is a different type of imaging to the long exposure deep sky stuff.
