If you've played the Dark Brotherhood DLC, you'll know that taking out contracts can be difficult. It can get you in trouble, you can get witnessed by someone who isn't even looking at you when you're clearly stealthed. You think 'By Sithis, how long will it take to get rid of this 600g+ bounty? Look at all these stolen items I have! I don't want to get caught on the way to an outlaw's refuge!

Worry no more, for I have some helpful tips on how to avoid some easily made mistakes and to not get caught (most of the time)

NPCs and Detection
'This contract is impossible! I'm surely going to get caught!'
That's where you are wrong. Patience, my child. All NPCs that you can be sent to murder are scripted to move to an area where they can be slaughtered without anyone noticing.
Watch for patterns.
There are three stages in an NPC's pattern, and here they are
- They fiddle with something out in the open. Perhaps they will go to have a look at a bookshelf, browse a merchant's store, look at a map, anything. Sometimes they'll stand in front of a desk staring at their bare hands.
- Then they move towards the 'safe' spot. Wait for them to stop. They'll stay there for more than long enough for you to wait for a guard to pass, go into stealth and perform an unapologetic gory attack animation. If you miss this and they start to walk away, LEAVE THEM. Wait for them to go back and mess around, then follow them back.

Watch out for guards and wandering NPCs. All neutral citizens are scripted, sometimes they will get a little too close for comfort. Don't risk it, they'll bugger off soon. Wait for them to get a reasonable distance and turn their back to an approaching crime scene.

Guards may walk by. Don't use that blade of woe until they're far out of the way.

Once it's safe, go in for the kill. It will take a while to get it right but eventually you will start to just 'know' if you're in a position to murder without witnesses.
I think this goes without saying, but stay stealthed. Both before you murder and after.

Preparation and Optional Tools
-If you have valuable stolen goods, fence or launder them before you kill. It's not so much of a big deal to lose some green or white quality stolen goods, but better safe than sorry.
-Keep 5,000 gold on you at all times. Put the rest in the bank.
-If you're not a Nightblade or you are a Nightblade with a very low magicka pool, Invisibility potions are your friend. If you want to make them yourself, here is a wonderful guide showing which alchemy ingredients can be used to make an Invisibility potions.
- If you are a Nightblade with a decent pool of magicka, invest a couple of skill points into that first skill in the Shadow tree that grants you invisibility. This is invaluable and can be used to approach your target for extra safety while stealthed, and to get away.
- Also, that passive which makes Shadow abilities last longer is great.
- Legerdemain tree has improved hiding, get that.
- Thieve's Guild tree has veil of shadows to reduce detection and Swiftly Forgotten if you get caught. Also Clemency if the guard catches up to you.
- Dark Brotherhood Scales of Pitiless Justice helps remove heat if you get caught. Also, Spectral Assassin can save your life
- If you're a Khajiit, put some points into that sneaky racial passive.
- If you're a vampire, put some skills into the 'Dark Stalker' passive
- Champion points that reduce sneak stamina costs are nice too.
- Night's Silence armour set reduces sneak movement penalty! However, as of the most recent patch, it seems to be bugged (or, hopefully not nerfed), but it might be fixed soon.

I got caught! Now what do I do?!
It's going to happen. You're not going to get away with it every time.
If a guard catches you and you are forced to raise your arms in surrender, DO. NOT. FLEE. Don't do it, it's not worth the extra bounty. Pay the damn fine. This is why I said to keep 5,000 gold on you at all times. The fine for murder is just over 600 gold, which is not a lot of money, especially endgame. A couple of awards you get for contracts will pay the bounty themselves.
This is also why I said to fence or launder valuable stolen goods before murdering.
If you insist on not paying the bounty, make sure to have Clemency (Thieve's Guild passive) and ones that cool down bounty and heat. In the mean time, go do stuff that doesn't require you to approach a city. If you need to sneak around, the aforementioned abilities will help you.

And that's a wrap! Hopefully I helped at least one of you get away with murder. If you found this helpful, give the post a +1 awesome, if you didn't, then don't.
If I've missed anything that would be helpful to add to this guide, give me a shout in the comments.

Now go out there, brothers and sisters, and obey the will of the Dread Father.