1) First, understand where they live and what the observing is like there. I live east of Seattle, where there is lots of light pollution, lots of clouds during the winter and long days during the summer. All of these impact how much you can use the scope

2) Understand your expectations about what you’re going to see, because if the gift is to somebody who is used to images from Voyager, Hubble, or Cassini, they are likely going to be disappointed. Yes, you can see a lot more than with the naked eye, but Saturn looks anywhere from something vaguely ovalish to a recognizable outline without a lot of detail.

+1 on joining a club and trying out some scopes so you understand cost/performance.

John travels all over the country (and world). If you get a chance, try to hear him speak or attend his telescope making class. He’s known as the barker of the stars for a reason. He was featured in the PBS documentary “The Astronomers,” and selected by Smithsonian Magazine as one of the 35 people who have made a difference http://www.smithsonianmag.com/people-places/dobson.html.

The money spent on purchasing today’s “made-in-China” (or other prison-labor or sweatshop countries) ’scopes would be much better spent acquiring the parts to actually assemble/produce one of your own. All it takes is a bit of time and patience – with a result usually far better than you’d expect, or the market can provide.

And, it isn’t all that difficult – as can be attested to by any winner of the children’s division of the Stellafane Annual Telescope-making Awards.

Similar things happen with every hobby that requires a degree of expertise: photography, chess, etc., so It’s good to know how to maximize the performance of something it’s impossible to return, whether for economic or sentimental reasons.

Most ‘department-store’ telescopes are limited more by their eyepiece optics than their objectives. Normally, these instruments come with a small assortment of eyepieces and accessories based on simple lenses, which results in narrow fields of view and image distortions. For a modest investment, low-end achromatic eyepieces can be bought from reputable on-line companies which will greatly improve the image.

Often, the department-store scope also has an eyepiece holder which only takes 0.965″ O.D. (outside diameter) eyepieces. It’s possible to get a ‘hybrid’ star diagonal which fits into 0.965″, but also accepts the more common 1.25″ O.D. eyepieces. Other 0.965″-1.25″ adapters are available for reflectors, too.

Next, much beginner frustration stems from believing exaggerated advertising claims, but this can be easily cured by better information. All 60mm objectives begin to show degraded image quality at 120X, a 3″ at 150X, a 4″ at 180X, all well below the commonly-advertised 500X+. Really, a beginner only needs 30X-40X for the vast majority of nebular objects, and 100X-120X for planetary detail. Even the largest instruments available to amateurs experience trouble at around 300X, because of the Earth’s atmosphere (which is why they put the big guns on the tops of mountains!).

The finder is another frustration; these are commonly extremely cheap low power refractors mounted in difficult-to-adjust housings. Fortunately, it’s possible to ‘upgrade’ to inexpensive red-dot sighting tubes which give better performance.

Finally, the infamously wobbly mounts can often be improved by simply tightening the screws, but suspending a 5-10lb. weight from the tripod head also helps.

Now, assuming that the original scope cost around $100, a ‘full’ upgrade might more than double the total investment (prices approximate):
inexpensive 1″ achromatic eyepiece: $35
inexpensive 1/2″ achromatic eyepiece: $35
0.965″-1.25″ hybrid star diagonal: $35
inexpensive red-dot finder: $35
weight & string: scrounge it
Many might not want to invest at this level to rescue a poor telescope, but the benefits would be immediately apparent. Certainly it would be better than putting up with all the frustration.

Finally, a caveat: if the scope includes an eyepiece-plane solar filter, put it on a sturdy table, take a hammer, and smash it. It is dangerous to use, since the objective-intensified heat of the Sun can crack it while in use, a fact made even more dangerous by the unpredictability and suddenness of the malfunction. We’re talking about blindness here.

Even the more-common solar projection screen causes enough heat to build up rapidly in the optical system to melt cemented lenses, so it isn’t recommended with most modern eyepieces and achromatic objectives.