Your bread and butter (BnB) rotation is Dragon Kick > Twin Snakes > Snap Punch. That is the core rotation. You replace Snap Punch with Demolish whenever the target does not have the DoT on it or it has run out.
Right off the bat you want to make sure you use Blood for Blood and Internal Release as your buffs on CD. You also want to use your 2 off-GCD attacks - Steel Peak and Howling Fist - on CD.
Throw Touch of Death anywhere in your BnB rotation if the target does not have the DoT on it or it has run out.
If the fight in question isn't very TP intensive (you don't have to worry about conserving TP) then first throw in Fracture whenever you can as well, similar to how you handle Touch of Death.
If you really want to maximize your DPS and don't have to worry about conserving TP, you can use Impulse Drive*.
General rule of thumb for skills such as Touch of Death, Fracture and Impulse Drive: be careful as these are not part of MNK's forms, and therefore need to be used with care to not lose GL3 stacks. After just refreshing GL3, you have 12s to get it back up. This means 6 skills with a 2s GCD. If GCD is above 2s, then 5 skills to be safe. Of those skills, 3 of them need to be your BnB rotation in order to get back to GL3, so you have 2-3 skills worth of time for Touch of Death, Fracture, and/or Impulse Drive.
Be mindful of mechanics in every fight. Anticipate if you will need to move soon, and in such cases forego using skills other than your BnB rotation in order to give yourself maximum time to refresh the stacks. If you will not need to move soon, use any of the extra skills as necessary.
When you need to burn something down with no regard for TP, and you've already applied Touch of Death and Fracture on the target, you can append 2-3 Impulse Drives to your BnB rotation depending on your cooldown.
( DK > TwS > SP > ID > ID > ID > DK > TwS ... etc)
* Keep in mind that Impulse Drive needs to be done from the rear. If not, it is a massive waste of TP and a net DPS loss.
Favor Crit Rating in your gear choices. Given a high crit rate, you can forego the use of Bootshine and stick to the BnB rotation that will allow you to stay on the targets flank, effectively minimizing your need for movement and risk of missing out on Auto Attack hits.
Hope that helps.