so in some couple days i will be going on vacation for new year and i'm planning to shoot some star trails at mountain(its mount bromo if someone wondering). so after doing some research about astrophotography, i've seen two ways of playing with the shutter speed, i see some that recommend doing it with shutter speed like up to 30s, for sure shutter speed that camera can shoot at and some other that use shutter speed above 30s, even minutes or hours, the one thing i wonder about using shutter speed above 30s is that how to get the correct exposure? do i have to involve some math by counting the stops or some stuff?? please help me as i'm really confused:)
another thing that i don't know is what the best time and situation to shoot star trails. i'm assuming as i'm going to shoot at mountain area, so cloud shouldn't be a big concern for me(?)
Always shoot away from light pollution and with no moon or 1/4 moon out. ISO 100 gives much better star colors. You should use an external battery pack and Id also tether with a laptop for 60 or 90 second exposures. Longer focal lengths will give much more movement per minute vs shorter focal lengths.
It would be good to practice at home before going on vacation.
There are a lot of good tutorials online, and I've attended a couple of workshops as well. I mostly shoot at 20 mm for night photography and have found that I start to see a little bit of motion past 15 seconds on a full frame camera (Canon 5DS R and a Sigma 20 mm Art lens) This is counter to the 500 rule for star trails that provide a rough rule for the Earth's rotation, so your experience may vary. If you want super crisp stars, I'd recommend adjusting aperture and ISO to keep your shutter speed as short as possible.
If you want star trails, my current preference is to take short exposures (15 seconds) and stack them. I don't typically shoot star trails, but I use StarStax (https://www.markus-enzweiler.de/StarStaX/StarStaX.html) and stack short images when I do. StarStax is free (Mac/Win/Linux) and offers an option of comet-style heads on the star trails, which can be a cool effect. Check out this article on star trails http://www.nightphotographyworkshop.com/articles-tutorials/star-trail-st... . This is on the site for the workshops I've taken, and Mike and Darren are excellent photographers and instructors.
Roger Clark has a comprehensive night photography article/training on his site. http://www.clarkvision.com/articles/nightscapes/ I agree much more with his 200 rule than I do with the more common 500 rule for star trails. TLDR notes for the 500 rule are that 500/lens focal length in mm = number of seconds before seeing stars "move" due to the Earth's rotation. So with my 20 mm, it would be 500/20 = 25 seconds. With Clark's 200 rule, it would be 200/20 = 10 seconds, which is a lot closer to my 12-13 seconds where I can normally see star motion.
One of the big things to remember is composition. You're taking a landscape shot, presumably, but with emphasis on the sky. Try to get something unique and well composed for the landscape because it will complement your sky shot well. There are several techniques for doing this, from light painting with an LED panel to taking a day exposure prior to twilight and compositing it into your picture. My favorite method is to take a very long exposure (20-60 minutes) of the landscape at night and use that to composite in the same shot taken in series. Look at Mike's Super Long Exposure Cheat Sheet on the Night Photography Workshop page for a ton of detail.
If you have a Mac, Starry Landscape Stacker is amazing, and it's the only paid app I'd recommend beyond Photoshop and Lightroom. If you look at my pictures on this site, I shot Delicate Arch at 12,800 ISO on a 5DS R and stacked 25 exposures per position (the picture is a stitched panorama). If you're running Windows, there's a free application called Sequator that does something similar. I haven't personally used it but I've heard that it works, though has some quirks.
When you're planning, there are a ton of resources online. Search for "dark sky maps" to look for light pollution in the areas you're thinking of. These aren't an absolute - I have some great pictures from places that show that they have a little light pollution. As Robert mentioned, having the moon out when you're trying to shoot stars won't be good. Sites such as timeanddate.com have moonrise and moonset calendars for your area.
On the Night Photography Workshop site, I'd recommend looking at the articles on Light Painting with an LED Panel, the Star Trail Stacking tutorial, and the Night Photography 2.0 article. I don't work for these guys, but I've learned a lot from them and they have a lot of great free articles, so that's why I've mentioned them as a resource so much. Fstoppers also has a tutorial that includes astrophotography (Photographing the World 2).