How do I stop the Riften Guards from killing me?

I'm not stupid: I know that the guards kill me when I commit crimes, but I don't know how to stop it. I saved before I stole the stuff, then I got caught stealing it and accidentally deleted my save. :(

Now all the guards in Riften attack me on sight, so I can't even go to jail or anything. My last save before the one I delete is like 4 hours of gameplay behind where I am now, and I really don't want to have to revert. How can I fix this problem?

Try sheathing your weapon. Or try using a calming spell on a guard.

Here are the standard approaches.

Getting arrested

If you have a bounty, guards from the hold in which the bounty applies will attempt to arrest you. If you run from the guards they will chase you. If the guards become hostile, you can yield by sheathing your weapon.

When you are arrested by a guard you have several options:

Declare Thaneship

If you are the Thane of a hold, you can declare this to the guard. This will immediately clear your bounty (if the bounty is less than 3000 gold), but can only be done once per hold (twice if the hold is captured during the civil war and you are made a Thane by the new Jarl).

Pay your bounty

If you pay your bounty, you will be immediately transported outside the nearest town jail, and all stolen items in your possession will be seized. Thieves Guild members have an additional option to pay a much lower fine, if they so choose. This additional option will allow you to keep stolen items.

Bribe guard

Thieves Guild members have the option to bribe the guard. The amount of gold required to bribe a guard is usually much larger than the bounty for small crimes, but less than one for murder and doing so will raise the Speech skill, immediately clear your bounty and avoid having items confiscated. The Bribe Guards Speech perk also grants you this option. Note, the bounty cleared is only for the crime you were recently caught doing. If you had some previous bounty as well, this won't get cleared.

Go to jail

If you cannot pay your bounty, you will be sent to the nearest town jail. You are able to keep one lockpick in your jail cell, which can be used to try to escape from prison. Escaping from jail can be much easier than in Oblivion with an option to pick the door or a loose grate on the floor which is much easier, however, escaping prison will still keep the bounty on your head. There are also other methods to escape, such as pushing down a crumbling wall. You can also pickpocket the jail key from a passing guard to escape the cell. However, it is still difficult to recover your equipment. To serve your sentence, simply sleep in the bed in your cell, and you'll sleep through your entire sentence. Depending upon the length of your sentence, your progress towards one or more skill advancements will be reset to zero. Unlike Oblivion, you will not lose any past skill increases; instead, it will take longer to obtain the next skill increase(s).

Resist arrest

Resisting arrest will cause all guards in the area to attack you. If you change your mind, yielding to a guard will make them attempt to arrest you again, presenting the same options. Sometimes, you cannot yield, and the guards will simply continue to attack. Using a strong enough Calm spell will stop the guards from attacking, though speaking to them results in an arrest attempt. Another method is to punch an innocent person, keep your fists raised and then try to yield again.

Persuade guard

Occasionally another option will appear if you have a low bounty. You can attempt to persuade the guard that you are not worth the effort of dealing with, due to your low bounty, and should be allowed to go free. Success is dependent on the Speech skill. If successful, you will raise Speech, but will not clear your bounty. If your speech is 75 or higher, this option will always be present (given that the guard has not been persuaded already). If you wish to persuade the guard again, wait 2 days and the option will be available again.

Bounty collector

If your bounty is above 1000 gold, you may be met by a Bounty Collector. Unlike the guards, they ignore the distinction between holds and will attempt to track you down regardless of which hold you are in. You have to pay him the bounty + 20% more as his cut. Your bounty will be erased as it would be when you pay to the guard, but you keep stolen items in your possession. If you kill the collector after paying him, he won't have that money in his inventory. Also, use his services at your own risk as the bounty may still be present in the hold that he collects the bounty from, even after paying him.

Bug

Occasionally, Guards will not recognize your attempts to yield and will continue attacking even if your weapon is sheathed.

Source: http://www.uesp.net/wiki/Skyrim:Jail#Go_to_jail

In order to stop guards from killing you when you commit crimes, I would recommend using techniques that apply to any opponent within the game which is killing you.

Level Up
Guards within Skyrim are a higher level than the player and their level increases as yours does. However, the guards only level up to 50. Once you are over that level your power level should start increasing enough so that guards can no longer kill you.

Note that when you are levelling up, you need to do so by using skills that will help you avoid getting killed by the guards. Using Blacksmithing and Enchanting to level up is easy, but it doesn't help with any of the combat skills that you need to survive.

Better Equipment
Having better equipment is essential for surviving an attack by the guards. Better equipment should come naturally as you follow the first step, Level Up. This is one place where the Blacksmithing and Enchanting skills do become useful, as they allow you to enhance your equipment which results in a higher level of surviviability.

It is important to note that this will involve min-maxing your character somewhat. You may want to play a Khaljit hand-to-hand fighter that wears only leather armor but that isn't the best option to take. You should be wearing the best heavy armor you can to go along with the Fists of Steel perk

Appropriate Skills
Focus on using the skills that will allow you to survive longer in combat and deal more damage. Light Armor, Heavy Armor, Archery, Destruction, Conjuration, One-handed, Two-handed, and Block all fall into this category. Alteration is good if you are playing a wizard character who doesn't wear armor.

Appropriate Perks
You will want to choose perks that either allow you to survive longer during combat, or kill more quickly. Agile Defender and Avoid Death are examples of perks that allow you to survive longer during combat. Armsman and Dual Casting are examples of perks that will help you defeat your opponents faster.

Tactics
Correct tactics will definitely help you survive against the guards longer. A basic tactic (which I assume you have been using) is "run away". If you get far enough away from the guards fast enough, they won't be able to attack you.

When you do engage the guards in combat, try to start attacking them from a distance to wear them down before they reach you. If you're able to use ranged spells from a location where the guards cannot reach you (ie - on top of a building) then you should have no problems taking them down.

If you are forced into melee combat, try to choose a location in Riften where there's not a lot of room for multiple guards to reach you at once. If you're only being attacked by one or two at a time it is much easier to kill them. Try to avoid fighting in the marketplace where you can get surrounded by many guards at once.

If playing on the PC, a fast way to get guards off your back is by opening the console and then targetting any guard and then entering the console command, paycrimegold. This will automatically pay your bounty and then teleport you to just outside of the jail of the hold the guard belongs to (stolen items will not be confiscated). About the paycrimegold console command (from UESP wiki's "Console" article):

paycrimegold <0-1> <0-1> <faction ID>- Pay the bounty for the faction targeted NPC belongs to (the bounty gold will be removed from your inventory). The first 0-1 choice refers to being sent to jail: entering 1 will let you be teleported to the respective faction's jail, entering 0 won't. The second 0-1 choice refers to keeping your stolen items: entering 0 means you do not lose your stolen items, entering 1 means you do. If you don't add any choice you will be sent to jail without losing your stolen items. The faction ID is needed if you can't target an NPC. May also help in case guards attack you on sight. Faction ID's are given below:

00028170 - Crime Faction Falkreath
000267E3 - Crime Faction Eastmarch (Windhelm)
00029DB0 - Crime Faction Haafingar (Solitude)
0002816D - Crime Faction Hjaalmarch (Morthal)
0002816e - Crime Faction The Pale (Dawnstar)
0002816C - Crime Faction The Reach (Markarth)
0002816B - Crime Faction The Rift (Riften)
000267EA - Crime Faction Whiterun
0002816F - Crime Faction Winterhold
xx018279 - Crime Faction Raven Rock (Solstheim)