Melee bruisers - halp?

Generally I play tanky DPS-type folks like Shyvana or Mundo, and occasionally a few squishier but more powerful champs like Riven and Jax.
I just need help on engaging in teamfights. Am I supposed to be a meatshield? Generally as Jax I try to take out their adc, but I tend to get focused and die rather quickly. Mundo can survive for a while but his only significant damage is with his Q. Shyvana can ult and cause a fair bit of damage, but most of the time I just end up dying first, but the teamfight is in our favor overall.
Basically I initiate -> I die -> My team wins the teamfight. Is this how it's supposed to happen?

Sorry for the noobiness, I'm only level 18 lol, started last month.

Chrome was being a dick and not loading my site properly, otherwise I would have responded sooner.  I used to play League somewhat seriously, but not that much anymore.  I'll help as best as I can.

Shyvana and Mundo first.  How are you building them?  Keep in mind both of them have a lot of mixed damage even while building items like Sunfire Cape, Randuin's, and Spirit Visage.  You tend to be able to tank a lot of damage, survive under tower and in teamfights, and push minion waves hard.  Their objective is essentially to initiate and tank, yes, but ideally you don't die, haha.  But if you trade your 1 death for your team's 5 kills, then you did a fantastic job, because the enemy team likely didn't focus your team correctly.  Ideally, tanky initiators will take a ton of the opposing teams damage and crowd control, save their team from taking the brunt of it anyways, and also not die.  

Riven and Jax are a bit different, Jax being somewhere in the realm of Fighter/Duelist, and Riven being that and also somewhat of an Assassin.  They excel, and I mean excel, at fighting one on one, especially with squishy champions since

1. Their burst is substantial early game, which usually allows them to secure early kills.
   
2. Their sustained damage, especially with the items you buy from those early kills, is great.
   
3. They both have stuns, which are valuable for dealing damage to enemy champions without much damage taken in return.
   
4. They both have very solid mobility options for getting in, getting out, and juking enemy skills.
   

These traits allow Riven and Jax to outduel many lane opponents, transitioning into a powerful and dominating midgame.  However, if underfed, they tend to find it difficult to do their intended jobs.  They either tend to push lanes solo, or splitpush as it tends to be called, and outduel any champion that responds to their splitpush, OR, they fight with their team and generally aim to land their stuns on priority targets, such as an AD Carry or AP Carry, and then follow up with their burst damage for the kill, and then follow up with their sustained damage for the rest of the fight.  If things go badly for them, Jax can jump to units or Wards, and Riven can jump to almost anywhere with enough practice.  

For builds, Jax tends to like Blade of the Ruined King and Trinity Force, since they synergize well with his kit.  For Riven, she tends to like Bloodthirster and/or Ravenous Hydra, since everything in her kit scales extremely well with Attack Damage, but she also likes cooldown reduction to get her skills' (in particular her Valor shield/dash) cooldowns as low as possible.  Since she does not scale with Ability Power, and she doesn't much like tanky items until a 2nd or 3rd major item (after Bloodthirster or Hydra), her cooldown reduction options are generally limited to Brutalizer and Ionian Boots.  However, some "expert" Riven players like Best Riven NA tend to not buy boots at all, focus on Attack Damage generally, and make up for her lack of movement speed with her Q and E, but that's a bit hard for new Riven players to do as a general rule.

If you ever need help, my in-game name that I currently use is Best Sakuya NA.  For Riven play, I would look into Best Riven NA or Megazero, but there's plenty of other Rivens out there.  

http://www.twitch.tv/bestrivenna

For Jax, I have two friends, Relius and Best Mokou NA, that are both very solid Jax players, who would probably be willing to offer some advice on how to use them in teamfights and whatnot. I know a solid Mundo player but he doesn't play much anymore.  For Shyvana, it's probably Best Mokou NA again. Also, another guy in here, Best Youmu NA, is a generally solid and knowledgeable player that could also offer good advice. All of them have accounts on the site, so I'll drop this link their way and see if they post.

Hope this helps!

Thanks, it did help considerably. My Riven play is getting better at least, I'm not dying as much lol.

I generally build Tabi, BotRK, Hydra and Spirit Visage on Shyv, and Tabi, Sunfire, Warmogs and Atma's on Mundo. The rest is situational.
My main problem with Mundo is that he can be countered by Ignite and Magic Resist. Oddly enough though, I tried support Mundo in a bot game (because I was forced into support and I wanted to try a weird choice while I was at it) and his peeling with his Q can really help get the ADC fed, although he brings no CC to the table as well.

One last question - how influential is top lane supposed to be? I usually just stick top for most of the game and farm/trade, unless there's a teamfight or something where I'll obviously participate. But how much impact does a top laner have overall? I've rarely carried, and rarely seen people carry, as top. Is the AP mid or ADC supposed to decide the game's direction?

In League, everyone carries, but there's a couple thing to keep in mind.  Most people early on will not have any idea how to design a teamcomp, and there's a lot to be said for having a better team composition than your enemy, or in some way countering their composition.  I've seen Mundos destroy teams by being literally unkillable and dishing out an incredible amount of mixed damage.  However, if there's nothing for the Mundo to tank damage for, it will feel like you aren't doing much.  League is very much a team oriented game.  I just did very well twice as Tristana, but in my third game, the enemy team had a Lucian, who could bully me late game, a Lissandra, who could blow me up with strong burst and CC before I could interact with her, and a Renekton, who can get huge and tanky and is very hard for me to hurt late game.  It was up to my team to peel for me, and that's usually where tanky top laners come into play.  Honestly, the best tanky items for Shyv and Mundo right now are Sunfire, Spirit Visage, and Randuins, everything else is pretty meh if you're top lane.

Also, top laners can often get so fed that they can splitpush lanes and kill towers alone with impunity, since they're usually manaless and either a solid duelist or too tanky to kill easily.

Jax and Riven, on the other hand, snowball and carry games hard or fail miserably more often due to the nature of duelists and how they work.  

If you ever want to play, just hit me up at Best Sakuya NA.  I will try to get you some videos of me playing the champions in question, but no promises, haha. I got stuck with mid this game, so I'll be playing Nidalee. Hopefully I can get top next game.