Life doesn't always hand us solutions to go with the problems and situations we encounter. If you're in a pinch, sometimes you have to use what you have, along with a bit of creativity and ingenuity, to get through it. No guide can address every possible situation that might arise, but here are a few general suggestions.
You can't anticipate everything, but you can anticipate many things, and the more you can prepare ahead of time, the more resources you'll have to draw upon when faced with a problem.
Build a tool kit and learn to use it. The more tools you have to draw on when met with a challenge, the more resourceful you can be. Depending on where you spend your time, the tools at your disposal could take the form of a true tool kit, or they could go in a purse, a diaper bag, a survival kit, a workshop, a kitchen, an equipment truck, or even your selection of camping gear. Learn to use your tools. Then, make sure you have them with you when you need them.
Practice at home. If you don't know how to change a tire, try it in your driveway before you get a flat miles away from home, in the dark, in the rain. Learn to pitch your tent in the back yard, or take a short day hike to get used to your backpacking gear. Refine both your tool kit and your skills before you must put them to the test.
Anticipate likely problems and deal with them before they become problems. If you worry that you might forget your keys and lock yourself out, hide a spare key in the back yard. Attach your keys to something large and visible so you don't lose them. Coordinate with others who are coming and going so you don't accidentally lock each other out.
Assess the situation. When a challenging situation does arise, try to clarify and define the problem as best you can.
How severe is it? Is this truly a crisis or merely an inconvenience or a setback? Does it need to be addressed immediately, or can it wait for an appropriate solution to be developed? The more urgent the situation, the more creative you'll have to be.
What is the nature of the problem? What is really needed? For instance, do you need to unlock the door, or do you need to get in or out? These are two different problems, since the latter might be accomplished by passing through a window, by climbing over or under a wall, by going around the back way, or by removing the hinge pins in the door. For that matter, do you need access at all, or could you get what you need somewhere else?
Assess what is available to you. Being resourceful is, above all, about clever, creative use of resources. Don't forget that resources aren't all objects. Do you have access to, or could you obtain, any of the following?
People. Whether you need bus fare to get home, good ideas, moral support, the use of a phone, or simply extra hands, involve others if you can. Brainstorming together may result in some great, joint solutions. Ask people you know and trust. Seek professional help. Or, as appropriate, ask anybody in charge (authorities, employees, docents, ushers), since these people often have access to additional resources. Even if you end up asking help of strangers, you will probably be pleasantly surprised by the results. If one or two people are not enough, could you form a team or task force? Could you persuade city hall or another organization to further your cause? "What separates those who achieve from those do not, is in direct proportion in their ability to ask for help." That quote was by the CEO of CocaCola as spoken in the movie "The Journey".
Communications. Could you contact somebody who might know the answer, lend a hand, etc.? Could you ask a question, get somebody or something started, coordinate, cooperate, or commiserate?
Information. Has somebody solved a similar problem before? How does the thing (or system or situation) work that you are trying to deal with? Which way is home from here? Whom can you contact, and how? How do you build a fire?
Money. It can't get you out of every jam, but it can be pretty powerful in some situations. If you don't have money and you need it, being resourceful may consist either of doing without it or of raising some. Could you ask people, hold a fundraiser, or get a job?
Objects. Don't be afraid to use these in unconventional ways. Wire coat hangers can be incredibly flexible and while screwdrivers aren't really intended for chiseling, prying, pounding, scraping, etc., they'll often do in a pinch.
Intangibles. Sunlight, gravity, and good will can all act in your favor and even be harnessed to your advantage.
Time. If you have it, use it. Again, you may need to figure out where you can get some more. Depending on the situation you need to overcome, you may need to work longer hours, ask for more time, enlist the time of others, implement temporary measures while you can develop something more permanent, be patient, or ask the patience of others.
Work backwards. Take stock of what you have available, then consider how you can apply it to the problem.
Break the rules. Don't go around carelessly disregarding the law, but do use things in unconventional ways or go against conventional wisdom or societal norms, if it will help. Be prepared to take responsibility, redress wrongs, or explain yourself if you do overstep your bounds.
Be creative. Think of crazy possibilities as well as obvious or practical ones. You might find inspiration for a workable solution in one of them.
Experiment. Trial and error might take awhile, but if you have no experience with a particular situation, it's a very good way to begin. At the very least, you will learn what does not work.
Use the situation to your advantage, if you can. If you missed the bus and the next one doesn't come for another hour, could you enjoy a cup of coffee or browse a store nearby while you wait? If the weather is freezing, could you use snow as shelter or ice as a building material?
Improvise. Don't box yourself into thinking that only a permanent solution will do. Use what you have at hand for a temporary solution. Fix your bike enough to limp home and do a proper job later.
Be an opportunist. If an opportunity presents itself, do your best to take it. Don't overthink.
Act quickly. Often an effective solution hinges on a speedy response. Be decisive, and once a decision is made, don't analyze, act.
Learn from your mistakes. If you had to scramble to correct a problem, take steps to make sure that it doesn't happen again. If you tried something that didn't work, try it a different way next time.
Be persistent. If you go away before the problem does, then you haven't solved anything. Try again, a dozen or a hundred different ways, if that's what it takes. Don't give up. Never consider not succeeding immediately as a failure - consider it practice.
Don't panic. Pressure may be a good motivator, but not if it's clouding your thinking. Think about why you can't just give up on this and that will give you the edge for the persistence you need to succeed.
Practice being resourceful before the pressure is on. Try cooking a meal with whatever is on hand in the pantry rather than going out to the store.
Invent what you need instead of buying it. Build or create your own, even if something is ready made and available.
Don't dwell on the past. If the root cause or original problem is something you can't fix, simply work to recover as best you can.
If you've jerry-rigged something to get through an immediate difficulty, make sure to do a proper job of repairing it as soon as possible.
Human contacts, like physical tools, can be collected in advance of when you need them. Networking, formal or informal, is one way to go about that collection. Also, if possible, offer others favors before you need to ask for any.