When healing, I highly prefer my Shaman over my Druid (especially this expansion).
Icy-Veins has a good guide, though.
When healing in a dungeon, it is important to remember that Restoration Druids have a lot of powerful tools to contribute to damage and crowd control besides keeping the group alive. Since the group is smaller than a typical raid, you will be able to produce a much more significant portion of DPS, which is essential in timed Mythic+ content.
A Restoration Druid’s priority should be keeping the group alive. That does not necessarily mean keeping everyone at 100% Health or aiming to do so at all times possible. On some packs and affixes, you can afford to heal your group between the pulls or let the HoTs tick fully without resorting to single-target healing spam. Judging the damage intake of the group is the most important aspect of your success as a healer in dungeons.
During light to medium damage, you should aim to keep 
Lifeblooms up. Try to heal low damage using 
Adaptive Swarm, 
Soul of the Forest-powered 
Wild Growths, and 
Efflorescence. Spend the rest of the time doing damage. Managing to cast fewer 
Rejuvenations and 
Regrowths without letting anyone die will be your biggest DPS increase.
During heavy damage, you should aim to keep up as many Rejuvenations as possible, always to consume the Regrowth HoT to power Wild Growth with Soul of the Forest whenever 4 or more players are not at full Health and, otherwise, cast Regrowth. Efflorescence is a good spell to cast if you can ensure 3 players will be healed by it. Placing it before the pull is the preferred strategy. 
Ironbark anyone who might be in danger liberally, as its cooldown is too short to sit on. 
Tranquility can be used as a strong cooldown when needed.