When playing runescape, everyone tastes the bitterness of defeat. I had lost a lot in those situations at times. However, I learned that its basically not just who is stronger, but who's better prepared for the occasion:

The New player-versus-player worlds are simply amazing! and thats for what you can earn! depending on your style of play, this can vary:

If your new to runescape: train until your combat level is in the mid or low 40's, once you get that done you want to get your fishing and cooking all the way up until you can cook lobsters. Once you can catch and cook lobsters, stock up on a full 28 slot inventory with nothing but lobsters. Head to a Player combat world and battle (is best to wait until your health is about to go into the orange, NOT RED!)until you are low or run out of lobsters. Rinse and Repeat as many times as you want or until you get killed. This strategy also works for any better foods also!

When battling on a Player combat world: ALWAYS take your kills food! it is a life saver!

When battling a person who wants you dead (and keeps coming back) DON'T!, maybe 2 or 3 times if your lucky or if they are very stubborn. It will be just a waste of food anyway trying to kill an opponent who has nothing good on him and keeps trying to kill you.

If you plan to go with a friend into a multi-combat zone, make sure you both are stocked full of food and are in each others level range because people would mostly go for the weakling of your group first before they target you! If your planning to attack another group, then that would be your objective. (for new players) If you run in to a combat area with a crossed-swords icon the it means its a multi-combat zone (more then 1 person can target you). For those of you who want to team up, this is where you want to be!

Safe Zones are areas where people can't kill you at. This goes for banks, certain towns and your re-spawn points. For new players, this would be shown as a skull with crossbones with a red "X" over it.
Hot Zones are areas where fighting is really tense! this is mostly for hard-core runescape players who want to make some quick cash or get some items real quickly. Hot zone are shown with a burning skull (skull with fire on it).
(Some of this is covered by the Player combat book you receive when you first visit a player combat world)

Other helpful player combat tips ( and for new players):

Walk, don't run! (always save your running energy to get away)
Don't go in to multi-combat areas alone (if no ones around, its best you keep a loaded stock of food just in case)
If you just started fighting in the combat world's, fight close to a safe area at all times!
If you lose your stuff, its not the end of the world! always keep close to equal or more then 10000g in the bank for to replace your stuff. Also make sure you arrange your items so you keep your most valuable items safe. However, if you get skulled in combat (will show as a skull and crossbones over your head), you cannot hope to see your most valuable items safe and sound if you die! It is best to let some one else take the risk of that then yourself (if someone else should attack you, you won't get skulled)
If you use range or magic, always keep distance between you and your opponent.
Best when you bring a friend along!
(this is for hard-core players) If you want to win against someone who has more food then you (with out prayer), keep a close count on how much food they eat during combat. Use only 1 just to keep you from dieing and don't use food to fully heal you (unless your opponent hits really hard, such as a strength pure) or else you'll run out sooner. Another way to get around this is to wait until after he finished with someone else (lessens the food he'll have) or switch to long range for a bit. Always use the prayer :save item on your prayer list at the last second if you are about to die! (must have a prayer level of 25 to use and conserves prayer points used)
If your one for the kill, try to "lure" your victims to a far away place before you initiate combat so that you can kill them before they reach a safe area. Be one for the surprise, especially in a very crowded area! It is also recommend you go for strength on this to help in killing people quicker. Attack is good, for it allows people to hit more and is great for long fights.(Lure: bribe, show where they can train, good place to find stuff at, and other ways you can get some one to follow you some where)
This is a "Dirty trick" that people will soon learn or have already learned : Taunting your opponent while in combat (it makes them more likely to type then to get their character to eat, which results as an advantage for you) (for new players: don't fall for this trick, no matter how much they bribe you or make fun of you ) This sometimes also goes for just simply asking on their status, cause it's affects them the same way but without being harsh on words to your opponent. Of course this also leads to people being more quiet while in combat, so its clear your going to win in a fight then feel free to do so.
(this also goes with the above stuff but I made it apart from it for a everyone gets annoyed or wants revenge at some point) Make sure you watch what you say in combat or out loud, for some one out there just might kill you for it.
I believe this covers all combat (in terms of non-members) in Player combat worlds. If your a member, using weapons with poison or special abilities will give you a great advantage in combat! Magic users : get ancient magic with your choice of the best magic armor/weapons and your good to go! Range users: Get the best of arrows and bows money can buy.