I often find that one place I am able to add the most value in life--whether personally, at work or otherwise is to solve a "new" problem. When approaching something that you or your colleagues do not know how to do, you are facing a new problem. The key first distinction is whether the problem is new to you, or truly new, as in no one has a really good solution.
The bevy of technology between Google and nearly all of the apps out there has made it far more trivial to determine if the problem is truly new, or just new to you. If others have an answer but you cannot find it, you might as well consider it a new problem. You may find collaborators later, but there will be a good deal up front.
The reason to distinguish between newness and new-to-youness is that there are drastically different solutions to the different problems. New-to-you problems have answers, and your job is to find them as quickly and cheaply as possible. Remember that anything built by humans (I am looking at you, software) has an answer. Someone, somewhere, made a choice that led to your problem. They may have also built a solution. They may have also disclaimed that they don't have a solution yet, but at least you will have your answer.
When facing a problem that is new to you, the first thing to do is look for someone else's answer. remember if you believe there is answer, you are very likely to find it. Do not exert effort trying to solve a solved problem. You are generally wasting your time an others. In the pre-Google days, this meant asking someone. It also usually meant asking the person who gave you the problem assignment in the first place. When someone assigns you work, it is because they do not want to do it. Asking them for help is fine (a later step), but gauge if they are in a teaching mood before asking for help. If so, ask away and learn it, and you better get it right after the teaching. If they are busy/stressed/distracted, Google it.
Step 1: Google it.
Start with the humble assumption that there is nothing special about your particular problem. Of the billions of people that have ever lived, assume many people have had this problem. A subset have solved the problem, and a truly blessed subset have written down an answer in the form of an article, blog post, software application, product or business service. Most new problems can be solved with step 1 alone. Most searches yield something worthwhile in the first 10 minutes. Be clever in your searches and learn Advanced Google Searching to speed things up and cut down on crap.
For proprietary business software, look through any help files, documentation and/or internal wikis for guidance. Respect your colleagues time-- if they spent time writing it down, respect them enough to read what they have written. This may seem to take longer than asking for help, but you can learn much more and no one else need be available so you can proceed with your work. Besides, once you get reading you never know what else you can find, or even how you can contribute to great documentation and save other's time.
Once you have found answer, find a way to remember it--either with memory, practice, bookmarking, notes, etc. Searching for old solutions may feel like a time waster, but not even remembering that there was a solution is an even bigger waste of time.
If you have not found an answer, proceed to Step 2.
Step 2: Ask someone for help
After you have done a reasonable amount of Google diligence (again, nothing in 10 minutes of clever searching and/or someone asking you for money are good signs you have done your diligence), it is ok to ask for help. There are two types of people you can ask-- Mavens and Connectors.
Mavens are people who know things. If you know them, they can get you the answer. They are usually the final common pathways. They are usually harder to find and/or reach. Do not be frustrated when they do not have the answer and do not know who does-- you just picked the wrong Maven, find another one.
Connectors are people who know people. If you know them, they know who you need to talk to. They are rarely the final common pathway, but can save you hours of time in finding the right person, and usually a tip on how to reach said person, what they like, the best way to reach them, etc. Respect the connector for their connections, and do not be frustrated when they don't answer your question directly. They almost never will. That is not why you called them. They provide value in saving you time in getting the people or resources with the answers you need.
Having a method to get to the people with the answer quickly, and obtaining their help is a valuable skill. In some ways, being worth teaching is the most worthy thing you can be. Being worth teaching includes humility, politeness, responsiveness to feedback, curiosity, acceptance of widely varying solutions, and respect. If you are worth teaching, you will find that you are continually learning. If you fail any of these-- arrogance, rudeness, discarding of different ideas, excessive expertise, disrespect--you will find yourself adrift without oars.
Choosing your method of communication is also important. For urgent and important matters, synchronous communication is required-- in person or phone. As you go down the urgency/importance, text message and "chat" (semi-synchronous modes) are appropriate. Email is next, real mail after that, and asking for help via Facebook message is just peculiar. Pick the least intrusive method that you can tolerate and still get your answer in the time that you need.
Distributed networks, fora, social networks, message boards, etc. are the intersection of Steps 1 and 2. When you cannot find an answer in Step 1, and do not know who to ask in Step 2, consider asking the internet. Be prepared for some gold and some garbage.
Finally, never fear asking for favors. It may actually be of great benefit.
Step 2 is often the end of your journey. If not, head to step 3.
Step 3. Consider spending a little money
Free solutions are always more attractive that solutions for money, but remember that your time is valuable. Spending small amounts of money to speed up a solution often far outweighs the cost. Don't spend a LOT of money yet, but spending $5.99 for an app that might work or $10 for an article, or $100 for an hour of someone's time may be incredibly valuable. If spending your own money, make sure it is with your budget (and yes, You Need a Budget, it will change your life). If someone else's money, keep within whatever guidelines they have spent.
If Step 3 fails, you may not be dealing with a problem that is that new. You may be dealing with a hard problem, possibly even a new problem. Stay tuned for Part 2...