You might know that the word 'planet' has its origins in the ancient Greek word for 'wandering star'. So the bad news is that you're trying to spot things that look like stars, but that move around and appear in different locations. The good news is that since they were known about thousands of years before the invention of the telescope, it means that if you're looking in the right place they should be easy to see.
Knowing what you're looking at
Unless you're very familiar with the night's sky, you're going to need some help telling planets and stars apart. Smartphone apps are a popular choice - such as Google's Sky Map on Android or Star Chart on iOS. The better ones will have a feature where you point the phone at something in the sky, and the map updates to show you what you're looking at.
It's also commonly said that planets don't twinkle - or at least they twinkle much less than stars. If you see something fixed in the sky as a solid point of light, then there's a good chance that it's a planet.
A very useful piece of free software is called Stellarium. Amongst other things it allows you to pick a location, time and date, and see what the sky is going to look like. The image below shows the simulation of the sky that matches the photograph included above.
Another thing that Stellarium offers is that if you select the object (e.g. Jupiter in the example above), it will show you the expected magnitude. This is a measure of brightness, but is opposite to what you might expect - with negative numbers being the brightest. You might have noticed the presence of the Sun during the day - this has a magnitude of around -26. The full Moon is also fairly obvious at night, and this has a magnitude of -13. A helpful table is available from the International Comet Quarterly; but anything with a magnitude of less than positive 3 should be visible to the naked eye.
Where to Look?
There are five planets that, if the conditions are right, you can see with the naked eye:
- Mercury, Venus, Mars, Jupiter, Saturn
Regularly checking the observing sections of websites like Astronomy.com and Astronomy Now will keep you informed when these planets and other objects are going to be visible. Planets don't appear to move a great deal each night, and so you'll most likely have a couple of weeks to try and spot them.
In reality planets are also restricted to certain areas of the sky. Ones that are closer to the Sun than the Earth (only Mercury and Venus) are called 'inferior'. The remaining planets that orbit further away are called 'superior'. Let's start with some simple facts - to see the planets it needs to be dark enough; for it to be dark enough you need to be on the side of the Earth that is facing away from the Sun. Straight-forward enough; but if you think about the layout of the solar system, then the consequence is that inferior planets will only ever be visible close to the horizon. Superior planets however could appear anywhere. This is shown simplified in the image below:
Something else that you're probably aware of is that the solar system is quite flat - like a giant disc. Go back to the photograph and Stellarium screenshot above, and notice how the planets (and Moon) are roughly in a line. In the same way that the tilt and rotation of the Earth causes the Sun to arc across the sky, any visible planets will roughly follow part of the same path, called the ecliptic. That greatly narrows down where you need to look.
In summary the five closest planets can be easy to spot with the naked eye. Keep checking astronomy websites for news of when planets are going to be in the right position, and use software and/or apps to help you know exactly where to look. Give it a go. They're our neighbours after all.