In the early game, you'll want to look for adventures that give good item rewards. Elder signs are nice, but they don't help you complete adventures later on. Mid to late game, if an investigator is low on items, have them do adventures that give item rewards. If an investigator has a ton of items, focus on tasks that give elder signs.
Related to the above, an investigator with no items will have a hard time completing any tasks at all. Don't be afraid to spend a turn at the shop gearing up if there's nothing easy enough for only green dice. If that investigator has no trophies and no items, Lost and Found is better than nothing.
Your top priority should be adventures or monsters that lock important dice. Green dice especially, but also the yellow and red dice if you've got a lot of items stocked up. Second priority is midnight effects. Both are pretty rare, thankfully. Those are the only two types of adventures that make other tasks harder, so once they're clear, you can focus on what gives the best rewards or is easy to complete for that investigator.
If you have a choice of what tasks to complete after a roll, do the hardest task. A lore and a peril task is harder than a single peril, and a two lore task is harder than either of them. Don't waste a lot of dice on investigation rolls, however; if you need 3 dice to complete a 5 investigation task, try to do one of the other tasks instead if you can. However, unless a monster is easy to kill, they should take priority over other tasks in a mission, as they stay dead if you don't finish the whole mission.
It may be obvious, but take note that the red and yellow die don't have terror results. The red die does have a wild card result however, which can be used for terror. Similarly, both the red and yellow dice have a lot of investigations, so try not to waste them on other symbols if there's a large investigation task that still needs to be done.
In relation to the above two points, don't give up on a task if you can complete it, even if you're using non-optimal dice to do so.
Don't forget about spells. If you've got a roll that can complete one task and go part way towards another, spells can help save that roll. Similarly, they can help you save more dice for another attempt if you fail the task.
I've only lost twice so far after about 15 games, and I'll vouch for all of the advice quoted above (and much of the rest in the thread).
Also, generally speaking I would say not to skimp on using your items and spells... I tend to use 'em when I've got 'em, even if it seems like the adventure has easy tasks. Better safe than sorry, so I'll pretty much always add the yellow and red dice if I can. A lot of times, you'll gain something back, anyway. Same thing with Clues. But that being said, use things wisely... for example, if you have an item that lets you change a die into a Lore result, and that's the last thing you need to get with a few dice remaining, go ahead and try to get it with a dice roll and only use the item if the last roll fails.
As mentioned already, note that the yellow die does not provide a Terror result. It's worth repeating, because I've caught myself a few times adding a yellow die to an adventure, only to realize that it was pointless because I was going for Terror. Along those lines, when discarding a die after failing a task, discard the yellow one if it is no longer useful (i.e., you only need terror). If you've focused a die or used a spell, use that die first to complete something, even if you rolled the same result on a new die that was rolled... you'll want to keep the others available as you re-roll to complete later tasks.
Sometimes you'll want to go to an adventure just to kill the monster there, to get it out of the way and get its trophy. You may take a hit for failing the adventure, but sometimes that's okay. But be careful to note the potential penalties of all adventures (including what Sanity/Stamina hits you may take from tasks) and whether your investigator can handle them, before starting them. But once in a while, you may need to sacrifice someone to finish an adventure (or to try to). Unless it's your last investigator, don't worry too much about that... In this version (as opposed to the dice game) a doom token is not added when that happens (I wish it was, though, as it seems like there should be more of a penalty for that). It can suck to lose the special ability (and items and trophies) of that person, but it's not necessarily that big of a deal in the big picture, especially if they accomplished something important on their last turn.
The adventures that capture dice are usually top priority for me, but also watch out for the "at midnight" adventures, in particular the one that adds doom tokens. Also, the one that takes 2 trophies from everyone ("The Curator") is particularly annoying to me and can be difficult to complete. If you get that one and don't think you can complete it, you may want to go buy something with your trophies before the Curator takes some of them. Sometimes you'll need to be patient and build up the right items from easier adventures or from the Souvenirs to succeed on the harder adventures, so weigh what's most important at the moment and what damage you can afford to take in the meantime. It can be better to be patient and take a midnight hit once or twice until you're ready to defeat that adventure, rather than unsuccessfully trying to defeat it a few times and wasting that time.
Take note of the invesitigator's abilities as far as what adventures they should focus on... Put Darrell on ones that require investigation rolls, Monterey on ones that give Unique Items as rewards, Michael on ones that require Peril results, Kate on ones where a monster is part of the reward or that have Terror effects, Joe on ones that give Clues as a reward, etc. Speaking of Michael's ability, remember that even if you don't need the Peril result, it can be used to get rid of a Terror result (if the adventure has a Terror effect). That being said, of course there will be times when a particular investigator will be needed on a certain adventure that's not their "ideal" type, but by and large, try to match them up to their best effect.