Okay, so that's a 130 mm newtonian with an f/5 focal ratio. Per the manufacturer's website, it comes with two eyepieces, 10 mm and 20 mm, giving 66x and 33x magnifications respectively.
First off, make sure your scope is collimated. The procedure is described in their generic Telescope Maintenance document, and also more specifically in the Astromaster Manual. See links on the site. The performance of your scope when observing planets depends a lot on collimation. I made it a habit to check collimation every time before I use the scope; I'm so used to it that it only takes 5 minutes now.
The topic of collimation is huge, just google "telescope collimation" and learn. I'm still learning new things after years in this hobby.
Once the scope is collimated, you could try to push magnification even higher, by using a 2x ... 3x barlow with either of the eyepieces - that would double ... triple magnification. Please be aware that more magnification is not always better; for any observation there's an optimal magnification, not too big, not too small. But I doubt your scope would do well above 200x, even though the theoretical limit is 260x. Probably not worth trying anything beyond the high 1XX values - that is, for your eyepieces, a 3x barlow.
For the Moon, any magnification works. Low magnification gives you broad images with lots of stuff to see. High magnification zooms into particular details. Good collimation is critical.
For planets, it depends.
Saturn looks good at any magnification. If you can see the rings, the shadow of the rings on the surface of the planet, and the main split inside the rings (the Cassini division) then you're doing fine. It doesn't have a lot of detail to justify very high magnification, unless you're looking for the finer ring divisions, but your scope can only see Cassini.
Jupiter is a bit tricky. It has enough fine detail to justify high magnification, but it has low contrast - and then as you increase magnification it gets more washed out, more dark, and hard to see. "Medium-high" magnification works best. Just try different eyepieces, with and without barlow, and see what works best for you. It also helps to keep your eye at the eyepiece, keep tracking the planet, and let your eye adapt - in time your brain/eye system will start pulling more detail out of the image. It takes me at least 2 ... 3 minutes to start seeing the really fine stuff there.
Mars - don't even bother unless it's at opposition. It only looks good when it's closest to Earth. The next Mars opposition is in July 2018, so there's a bit of wait until then (will start to look good a few months before that). Even then, you need several things to see Mars well:
- very high magnification
- excellent collimation
- a good instrument
- excellent seeing (the inverse of turbulence)
Otherwise it just looks like a red dot.
Seeing will affect all solar system objects (Moon and planets). When seeing is bad (when atmosphere is turbulent), any object will look bad. It depends on the weather - not just weather at ground level (what you think of as "weather") but weather in the whole thickness of the atmosphere, all the way up (the stuff only airplane pilots usually care about). If you live in North America, the Clear Dark Sky site can give you a prediction of a few parameters including seeing. When seeing is bad, high magnification is worthless (the image is fuzzy and keeps shaking like jello).
Another thing that helps: if there's a large temperature difference between inside and outside, leave the scope outside for a while to catch up with the air temperature. This will reduce internal turbulence and improve image quality on planets. I always leave my scope at "outside" temperature for about 1 hour before observing. When there is no temperature difference between inside and outside, then don't worry about this. This is like seeing (turbulence), but inside your scope.
Please note that light pollution has absolutely no effect on solar system objects (see below re: light pollution). Even when light pollution is very high, the Moon and the planets still look the same.
Dark adaptation does not matter for solar system objects (see below re: dark adaptation). You don't have to be in a dark place when observing them. I've looked at Saturn from a sidewalk under the bright lights downtown (city center), with cars and people passing by - no problem.
Deep sky objects (nebulae, star clusters, and galaxies), a.k.a. DSOs, are different.
These are objects with low brightness. Because of that, your eye cannot see details or colors. Collimation is less important. Seeing also doesn't matter much. Collimation and seeing affect fine details, but you can't see fine detail in DSOs.
What does affect them is light pollution - the light from all sources around you, glowing in the dust, water drops, etc in the atmosphere. This is why it's hard to see DSOs from the city. If you can drive 1 hour away from the city, to a place far from sources of light (cities, factories), then DSOs are easier to see.
Google "light pollution map" and you will find several sites that give you light pollution intensities in your area.
But even from the city, there are many DSOs that you can see. M31 (the Andromeda galaxy), the Orion nebula, the M13 cluster, the Dumbbell nebula - all these are clearly visible in an instrument like yours even from very light-polluted places. I've watched M13 many times from the middle of the Silicon Valley.
The trick is how to find these objects. Get a book called "Turn left at Orion" - it's a guide for beginners showing how to find many DSOs. Get a good planisphere (star chart) like this one and keep it next to the scope when you're observing DSOs. Start with something easy like the Orion nebula.
Also you could google "how to find the Orion nebula" (or M13, etc) and you'll find online guides which are sometimes helpful.
Usually you don't need high magnification for DSOs. Low and medium magnification work well - but it depends; e.g. I've watched M13 in high-ish magnification and it looks good. What really does help here is eyepieces with a wide field of view, because it makes it easier to find the objects. I'm guessing your eyepieces are of the Plossl design, with a 52 degree FoV, which is fine, but more is better for DSOs. Now don't go ahead and buy some fancy expensive eyepieces - keep them proportional in price with the scope, and the original ones should be fine for now.
Another thing that really helps with DSOs is telescope size - bigger is always better. That's also true for solar system objects, but it's even more important here.
Finally, make sure your eyes are dark adapted before looking for DSOs. Observe from a dark place, and stay in the dark for at least 15 ... 20 minutes before observing. Do not use anything with a screen (smartphone, computer) because that destroys your dark adaptation. Do not use flashlights. There are flashlights for astronomers, with a red LED and a dial button, and you need to dial down the light to the least amount that allows you to see and read the star chart. Very weak red light will not destroy your dark adaptation. You could also improvise a red flashlight, but make it as weak as possible (or put a dial button on it).
Clear skies to you and good luck!