Don't stand in her ult. Ever. The only reason to be there is that you were stunned, rooted or pulled there. Trying to charge through it will, most often, get her an easy kill.
It widens at the furthest edge. That means trajectories moving toward MF and to the sides of her ult will probably get you out quicker. It comes in waves as well, so the faster you get out the more she's out the power. Since it's AoE, if she has Death's Dance then you want to measure if it's safe to engage-- multiple targets will help offset the AoE penalty DD suffers and will punish all of them for committing if they don't do so swiftly and pointedly to end her ult (bring an Annie stun, a Sona R, Jax's E, Quinn's E, save Ashe's R for it...). If you do get caught in it for too long, cut your losses and run. Better to lose the objective than to die, lose the objective and possibly your lane.
If your chosen champ lacks reliable hard CC (stops actions [stun, silence, knockup] = hard) then you need to realize that her ult is going to give her a distinct advantage and avoiding it will rob her of some (or most, or all) of it. Besides her ult, she specializes in dealing with multiple foes so isolating her is a good approach, while if she's ahead you can stop her up with some linked CC-- she has no inherent defense and only a point-placed slow on a rather steep cooldown until late. Lastly, she has a lot of options to keep enemies at the distances she wants in lieu of CC-- the slow has a high range and a fairly wide area, it starts out fairly high at base and she comes part and parcel with passive movespeed-- so if you can't claim the element of surprise, discretion in engaging will keep you from falling into ults.
If her support is high-CC then you need to consider removing them from her (separating or killing), while if her support is high utility you need to force them to bail her out constantly so that they cannot use it to press the attack. If you can kick her support back to base, as well, with constant harass then you can try to line up a gank or get the kill by your own wit.
Finally, if her self-healing is indeed what keeps her alive then buy Grievous Wounds (either the Executioner's Calling 
for AD, or Morellonomicon 
for AP and focus on keeping your health up, and hers low. You might not force a kill but if you can force her back to base, you can earn some leg room.
When all else fails, consider the above and try a champion with a little more to throw against her (whether you're support, ADC, jungle, mid...)-- she has problems dealing directly with hard control and engage, especially if she's forced to or chooses to use her options up early in the fight. Most of her power is on cooldowns and she doesn't exactly have the on-hit stim anymore (read: prepared for multiple targets).
TL;DR: The closer you get to Miss Fortune with all your cooldowns, and the fewer of hers she has up, the higher your chances of winning. She does not like stuns very much as they cut into virtually everything she does. Remember that the game is won by pushing in the enemy Nexus, not by getting sick noscope killz with skillz.
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