IN GENERAL What i find is that you initially lane with someone, try and make it someone who can lane by themselves, then once you get level 5, you go back and buy a vampiric scepter, then you jungle until you are level 8. Once you have both buffs,(golem buff so that you have faster cooldowns) which works great if you need to run away from a fight you have your spinny move every 6 seconds. Anyways, after you have both of your buffs you move into a lane, and play gank. You gank were needed, and if ganking isnt working out, get back to laning with your teammate. This works well because it gives your lane partner who is laning by himself a chance to level much faster while you arent in his lane. Thus everyone is overall a higher level. I would recommend getting dragon at lvl 11 or 12 depending on how many of the suggested runes you have bought. The thing that makes tryndamere so good as a character, is the fact that he is one of the best late-game characters. This means that when everyone has close to their full builds you will destroy. Any character that is range ( such as: vayne, ashe, kogmaw, fiddle, caitlyn, etc..) will get dropped in 2-4 hits if you have full fury. In terms of how to keep yourself always full of fury, i would suggest that you attack the minions real quick to reset the countdown, and remember, before you gank, or go into a team fight, i would suggest hitting some minions before you go. The lifesteal will make your health go up and then when you get into the battel you will have full fury and you will also be able to hit higher with more fury. Baron: once you have your full build [or close] in the game it is often people think they can take out the Baron alone. False. I have tried and come close, and it may be possible if you get some luck, but overall you will need someone to take some of the damage, with full or close to full build, and at least 1 teamamte, baron should take less than 20 seconds. which is another huge advantage.

Someone runs away This is when you use your W move.. Which slows them down. As they are slowed spin over them and start hitting them, as long as you have full fury and they dont flash they are dead. IF they do flash, then use yours to chase them and finish.
Someone chasing you. This can be really tricky, but your E can spin through walls, so if you are running near the water, go into the dragon pit, and then spin through the back of the wall and get away. (dragon or baron) Utilize the golem buff so that you have it more often and then you can always get away.

Undying rage undying rage is tricky, if you are using it to finish a few kills then here is how. Use it when you are about to die, but dont get to greedy with it, make sure it is close, but then again you dont want to die because u forgot to press a button. Anyways, once you have used it, hit one person at a time, and go for the one you know you can kill, if you need to get away afterwards, then use your Q and your E so that you gain enough health back to take a hit, and then use the E to spin to safety. Remember that with the life steal build, there is no need to recall every time you are weak, just hit some minions or neutrals and get yourself full fury and full health all over again.

Late game pushes. One great thing about tryndamere, is that he pushes up a lane incredibly fast. For example. lets say there are 3 down on both teams as a resulty of a team fight that just finished in middle, and you have 45 seconds until they respawn. What you do is find the furthest pushed lane, and you kill all the minions. You push the lane so fast because tryn will 1 hit all of the minons with this build, and you spend no time fighting minions. with 45 seconds you can make a push from your inhibitor turret all the way to their inhibitor turret no problem (taking out 2 turrets or maybe even all 3 on your way) not to mention that if you havent gotten your full build by then, than all those minion kills will give you a huge amount of gold.

team fights Tryndamere is great for team fights, but its best to use him to gank a team fight, because most people flee if they see an even team fight with tryndamere involved. So once you gank, you need to determine if your team is winning the fight or not, if they arent use ur W right away, then proceed to attack. IF they arent losing and they start to run when they see you ganking, utilize your W to slow them and then spin and finish them off.
Using tryns combo of spinny and chicken will get you easy kills.

More early game tips if you are trying to get level 5 in an early game lane fight it can be very difficult. If they have any sort of character with a ranged attack it will be annoying as they will likely harass, It is extremely important that you dont die in the beginning so play very passive. If they get you weak with some hits then use your pots wisely, those 3 pots are meant to get you to level 5 without recalling at all and hopefully in a speedy manner. If they are making it hard to kill minons, then try and stay in the grass, and only go for the minon kill when you have your spin. Also, try to only go for the minon kill if it is going to be the final blow, this gives you the gold, and more fury, which helps when you heal. [Q] remember: if the turret is killing the minions for you, you get the same xp, so it isnt necessarily a bad thing if they push you that far back. Because you will get xp faster.

Jungling Once you get level 5, go back, by the vampiric scepter and start jungling. Start with the wraiths {they are on the side that has 3 neutrals} then move from there to the golems, then to the dogs. If you are weak (less than half) go back and get full health, if not, get the first buff, the golem buff, once you get both buffs, you should have killed all 5 sets of neutrals, and you will be level 7. Finish up the ones that spawned, and get back to laning, or go ahead and attempt a gank if you see an oppurtunity.

Dragon Dragon is important because it gives your team 1k gold, which is important. If you are not level 30, i would wait until level 12 when you have full health. (of course if you are somewhat fed, and have extra stuff then go for it earlier} but genearlly you should kill it at level 11 or 12, that way you get it before the other team. Unless your playing a good team they most likely wont even notice you got it so early.

hang in there tryndamere is one of the hardest early game characters, because the range chars tend to easily get you. but once you get to level 14 and higher is when tryn becomes fun, proper use of all of his abilities will result in you always winning 1v1s and usually 2v1s. Make sure you play smart and stay focused. and most of all have fun