I got an oil change awhile back, I notice my car idling a little more. Where I park for work it was hard to tell what the oil leak was coming from on the ground. I don't know much, but I popped my hood and the dip stick was not fastened, and oil was spewing everywhere. Now my spark plugs that are under my coil packs are covered in oil (from the bottom actually) and when my car idles down it shakes more. I tried to clean everything the best I could. I know I should get nee spark plugs and so on. Main concern is how so much oil got to the bottom of the spark plug where it screws in? Could I have damaged my engine? There is no knock. Could it be flooded?
If the oil looks like it could have come out of the open dipstick tube, which is entirely possible, then I would suggest that you get the engine thoroughly cleaned using a jet wash and engine de-greaser so that you can see if any more oil appears from anywhere else. (Don't hold the jet wash lance too close to the engine in case you force water passed any rubber seals though)
There is no point performing any work on the engine until you identify exactly where the oil came from.
Also check the oil level regularly to make sure you don't cause any damage to the engine.
Oil being pushed out of an open dipstick tube could be normal for the engine if the dipstick was not fastened in correctly, but it could also be an indication of the crank case ventilation system being blocked or even a sign of a worn engine allowing too much combustion gas to pass the piston rings.
Check the oil level, get the engine cleaned and keep an eye on it, then report back with any sign of more oil escaping.
Oil contamination can cause rough running, if you clean it off properly it should be fine. You don't need to replace your spark plugs, they won't be damaged by oil. The rough running is most likely due to oil contamination causing electrical problems, for instance fouling the contact between your coils and plug terminals. You could also have contamination where the ignition cables connect to the coils, or the coils could be soaked by oil in which case you'd need to replace them.
So start with a thorough cleanup of the engine and get all the oil off where you can, then use a cleaner to clean the contacts. Once that is done see how it runs. If you still have problems check on your ignition cables.
There are other things that could have gotten contaminated by oil, for instance sensor connections. A close examination backed up by a check of your OBD codes is a good idea to catch any other issues.
You don't mention what kind of car this is, but the crankcase ventilation/recirculation system on many modern vehicles is such that the fuel/air mixture will be a little bit off if the crankcase is not more or less sealed from the atmosphere -- for instance if the dipstick tube is not inserted all the way.
This would explain your rough idle -- the oil spraying everywhere out of the dipstick tube is somewhat to be expected, but could also be a sign of excessive crankcase pressure due to either of:
a) blowby due to worn piston rings
b) a clogged PCV valve or crankcase gas recirculation system
GM 4-cylinder engines are quite known to experience the latter in the area of 100k miles or sooner (see here); note that although the TSB applies to model years ~2010-2013 the underlying problem still exists in newer engines.
This would be good to attend to, as excessive crankcase pressure may have caused the dipstick to blow out, and if the dipstick doesn't blow out could create an oil leak around the crank seals.
You can test it yourself roughly by pulling the dipstick with the engine running and putting your thumb over the hole to see whether there's pressure or suction -- there may be slight pressure at idle, but if you rev the engine to ~1500 rpm there should be vacuum causing your thumb to stick to the dipstick tube a little bit. I'd suggest getting a mechanic to take a look if you are at all suspicious; it should be cheap, and fixing the problem can be a bit involved so you will probably want it done professionally anyways.
The oil around your sparkplugs is probably not a big deal, although it's not exactly great for your coilpacks etc; "clean it up as best you can" is the best bet here. If you have a shopvac (that you don't mind getting oily) you should be able to suck most of it up with a small nozzle.
If you can add the make/model of your car to the question, it may be possible to provide some more specific answers and possible DIY advice.
I got an oil change awhile back
How far back? How much driving have you done since then?
I notice my car idling a little more.
Hmm, a simple oil change shouldn't cause this.
Where I park for work it was hard to tell what the oil leak was coming from on the ground.
I don't know much, but I popped my hood and the dip stick was not fastened
Who changed your oil? I would go after them for damages.
and oil was spewing everywhere.
It definitely makes things dirty but dirt isn't inherently an issue all by itself.
After putting your dipstick back in place did you check your oil level? How low was it? I hope you've topped it off.
Now my spark plugs that are under my coil packs are covered in oil (from the bottom actually) and when my car idles down it shakes more.
This is likely not responsible for the shaking unless it's interfering with the operation of the spark plug. Odds are you would be getting a check engine light and cylinder misfire codes.
You've been low on oil for an indeterminate amount of time, you've possibly damaged your engine. Top it off with oil and see if it stops shaking.
The oil in the spark plug wells is due to the seals failing and needing to be replaced. This is not that unusual. It is unlikely you have done any harm to your engine. If it were to get bad enough you would have experienced a misfire and a check engine light would have come on.
Replace the well seals and since you have to remove the valve cover to replace the well seals you might as well replace your valve cover gasket as well. Often times the valve cover gasket and well seals are sold as a bundle.