When Erin Adams decided to leave the Portland, Ore., area and consider cheaper locations, she prepared to sell her secondhand 2005 Toyota Scion xB for something a bit more capable of hauling her belongings.

Ms. Adams, 41 years old, who works as a technical writer for an automotive safety agency, had seen reports of the red-hot car market. Earlier this month, she posted an ad to Craigslist—“Manual transmission, 81k miles, Shiny!”—and received eight offers in her inbox within 24 hours.

After the eventual buyer found out the car needed a new clutch, Ms. Adams ended up reducing her asking price from $4,000 to $2,800. “If it hadn’t been for the clutch, I would have sold it for what I bought it for 3½ years ago,” says Ms. Adams.

Ms. Adams joins a rush of consumers vying to make a profit by selling their vehicles as prices for used cars and trucks have skyrocketed. Over the past 12 months, the index for used cars and trucks rose 41.7%, according to the consumer-price index. Prices for new vehicles rose 6.4%, the largest jump since the period ending January 1982.

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According to J.D. Power, that amounts to an average used-vehicle price increase of $5,000, creating a rare opportunity for consumers to sell their used vehicles, a notoriously depreciating asset, for perhaps as much as they originally purchased them or more.

There are signs that the market is plateauing—prices rose 0.2% for used vehicles in July, compared with substantial increases in recent months—but experts don’t expect a drastic drop soon. As the global computer-chip shortage continues to limit the number of new vehicles for sale, requests for appraisals on Edmunds.com have risen nearly 40% for the past two quarters.

“Everything is bonkers,” says Tyson Jominy, vice president of data and analytics at J.D. Power. “It’s something that we’ve never seen before, and I don’t know if we ever will again.”

Here is what you need to know before putting your wheels on the market:

A global chip shortage is affecting how quickly we can drive a car off the lot or buy a new laptop. WSJ visits a fabrication plant in Singapore to see the complex process of chip making and how one manufacturer is trying to overcome the shortage. Photo: Edwin Cheng for The Wall Street Journal The Wall Street Journal Interactive Edition

Do you need a car?

The first question all prospective car sellers should ask themselves is whether they will need to replace the car they are selling.

“Individuals best able to take advantage of this opportunity are those that have an extra car,” Mr. Jominy says. “Doing it for profit in a situation where you need your car or both cars in your household means you’re going to have to be back on the car market,” where the average transaction for new vehicles recently surpassed $40,000, up nearly 15% from last year.

Consider your situation when it comes to your household finances and transportation. For example, when will your employer require you back in the office, and what will your commute look like? If you live with your partner, can you both commute comfortably with one vehicle?

If you have a vehicle you are happy with—say, with unique customizations or a rarer make and model—think twice about selling. It may be hard to replace it with something similar or even comparable, and you may end up stuck with a new vehicle you don’t like.

Additionally, certain nonconventional vehicle colors, such as yellow, are likely scarce right now, says Mr. Jominy. “What’s being built are things that are going to move instantly,” he says.

Prepare and be ready to negotiate

With any auto sale, enter negotiations with as much data as possible. In addition to visiting sites such as Vroom or CarMax for an appraisal, sellers also benefit from getting multiple quotes for repairs needed.

Presenting the buyer with a range of the costs might result in less money out-of-pocket for the seller to make repairs or less money that the seller will have to knock off the asking price, says Ivan Drury, an automotive analyst for Edmunds.com.

“You want to be able to tell someone, I’ve got three quotes,” says Mr. Drury. “You might sacrifice a little bit of profit potentially, but at least you’re on a level playing field with whomever you’re speaking with.”

Calculate what you really stand to profit

Your car’s sell price is affected by more than your quote minus repair costs.

Sellers should get up-to-date on how much they owe on their loans. Depending on market conditions, the terms of the loan, and how much is left to pay off, you might find that you owe more on the car than it is worth, says Matt Dundas, director of finance at Carvana Co.

Conversely, at the current rate of appreciation, you might find that you can sell your car and have more than enough left to pay off the loan, he says, “which has been kind of driving more people to consider and explore selling their car.”

Additionally, most states offer some form of tax credit for vehicle trade-ins, Mr. Dundas notes. So if you are looking to profit from your current vehicle by upgrading into another, look into your state’s tax-credit policies, which can vary depending on the state’s sales tax or even dealership location.

What if I am near the end of a lease term?

Mr. Drury urges consumers to check the terms of their vehicle lease before attempting to sell.

Some auto financing companies have tightened rules around how long lessees have to wait before unloading their car or truck, forcing some lessees to first buy the car outright, he says. Contact the financing company and familiarize yourself with the terms.

If a dealer can work with a financing company, they will have an incentive to offer more favorable terms because they can get a payment for setting up your loan to purchase the car. But Mr. Drury advises consumers who are currently leasing and want a new vehicle to just go back and do it again.

“It’ll probably be the absolute cheapest way to get another ride right now,” he says. “Slide into the cheapest lease you can to hold you over until inventory right-sizes itself, and then you can go and find that blowout sale and all the stuff we’re accustomed to seeing.”

Decide how you will sell—dealer or direct?

Lastly, if you decide to sell, you need to consider what offers you will get—and where.

Some dealership groups might be so hungry for used-car inventory that you might find the highest offer there, says Mr. Drury. Sites like Carvana and Vroom may have competitive offers as well but will pick up your vehicle directly from your driveway. A representative from Carvana says the company bought a record number of cars from customers in the second quarter of this year.

Whichever you choose, be mindful that things can always change in the future, says Zarak Khan, senior behavioral researcher with Common Cents Lab, a research lab at Duke University that focuses on financial wellness.

“If you’re thinking, I have the opportunity to get this sort of immediate gain and you’re balancing that against the future benefits of flexibility around transportation, you probably aren’t valuing them as highly as you should,” he says. “The main bulwark against selling is probably just the friction involved.”