There are a few main pointers when buying an expired domain, you have to consider your budget, the domain length, the appeal and potential of the domain, estimated value and historical use. These values all play a part in determining if the domain has the potential to be transformed from a barren wasteland into a successful brand.
Your budget
The first and most important step is to have a clear budget and to know when to walk away from an auction when the price is out of your range, this can be difficult as the fear of missing out can really play on your rational decision making. You'll be thinking 'oh, I just need to beat this other bidder', 'it's only x amount of dollars over my budget', this emotional bidding can quickly turn into paying way over value for a domain. it's good to develop this habit over small monetary things so you don't find yourself over bidding on a house or car. Personally I only go for domains under $20 AUD and my strategy has changed to only bidding in the last 2 hours of an auction, which vastly increases my win rate. Occasionally you can get lucky and snag a decent domain for under $10 AUD in the buy now sections, but you have to be very quick.
Domain length
The second factor to consider is domain length, generally domains shorter than 12 characters are worth more than longer domain names as they are easier to remember and type. While looking at domains, you'll eventually come across Number domains, these are very popular in China as the numbers can stand for words and phrases, and are generally easier to type and remember. Unless you know what they mean, I'd probably stay away from them as a bad combination of numbers will be extremely hard to sell as the target market is limited.
Name appeal
The third factor is the appeal and potential of the name itself. Is the domain name memorable, catchy or represents a niche interest? Then it will carry more value and meaning to your audience than a name that is more generic. Occasionally the domain extension will be incorporated in the domain to form a word or phrase, these can command higher prices and also be more expensive to host.
Domain value
The easiest way to get an estimate is to go to GoDaddy domain appraisals and type in your domain. GoDaddy will spit out an estimated value and give you a few similar domains that have been sold recently.
Historical use
Another thing to check is the historical use of the domain via a site called The Wayback Machine, this site provides visual snapshots of the domain throughout it's use and can help you determine if the site was actually active with meaningful content and backlinks or if it was a parking page. This will have a large effect on its overall value as well.
More in depth statistics
Serious buyers looking at domain investing can use websites like Semrush or Mangools To get more in depth statistics like number of backlinks, backlink content, historical site traffic, keyword tracking to determine the next popular domain names and a myriad of other things. These tools can cost a lot of money and some are not beginner friendly, but they can give you valuable insights as to your domain's history and ideas for metadata keywords to boost your SEO.