Before releasing a Puppy’s Final version, its Dev has tested it on the computers he/she has available. (S)he has probably published one or more Release Candidates (-RC), received feed-back from Puppy-Fans/Testers having other computers, and made adjustments. Applications which are included in that Puppy are among the things tested: Did they work? Did they conflict with other applications?
Your Puppy is a finely tuned operating system. And now you want to screw things up by installing some cockamamie application which will remind you to walk your dog. 
Well, its your computer. But let’s try not to make a bigger mess than the dog. 
You’re tempted to open Menu>Setup>Puppy Package Manager, plug the name of an application into the Search box and click Auto-Install. Don’t. Not only will Puppy Package Manager Auto-Install applications which may not work out-of-the-box, even if they do work they may not be the best application for your task under your Puppy. For example, both Openshot and KDEnlive are top-notch and similar video editors. If you’re familiar with one, learning how to use the other isn’t very difficult. Under Xenialpup Openshot was your best choice. But under Bionicpup, KDEnlive just works better. Ask yourself, What do I want to accomplish? Then exercise some flexibility in your choice of tools.
The first places to look for Applications are Menu>Setup>Quickpet. [Not all Puppies have this]. Quickpet is a repository of applications your Puppy’s Dev has tested but not included. There is one exception to applications available via Quickpet I don’t recommend: Wine. Wine is both a work of art and a continually evolving target. We are fortunate that we have a dev, version2013, who specializes in publishing wine applications. Before installing any wine available just for your Puppy, examine both the Wine thread for the latest advice, viewforum.php?f=142 and your Puppy’s thread for posts revealing successes and problems.
The next place to look for Applications is on The Forum’s Additional Software Section. The Section is divided into categories almost identical to those which appear on your Puppy’s Menu. Within each Category are Threads discussing applications of that category type. Especially if you are new to Linux, you may not be familiar with some of the best applications –as good as, sometimes better than those you would have had to pay for running Windows. But even if you’ve been using Linux for years, remember Linux is Open-Source. Someone or Group frequently decides “I/We can do it better” and publishes a new, and sometimes better, application to accomplish the same task. Moreover, this is Puppy. The best application under a Puppy may not be the most often touted application for the ‘Big Boy’ Linuxes.
You probably know Google-Chrome. There are versions which run under Puppies. It’s a good Application. Occasionally I use it myself. But for many Web-centered tasks you may engage in you’ll find several Chromium-Clones that will perform as well and provide greater privacy. They are on the “Browsers and Internet” Subsection of the Additional Forum Section. Applications offered on the Additional Software Section have a major advantage over those you might install using Puppy Package Manager. Someone has taken the time to create an application which runs under Puppies. That isn’t always the case with applications you can install via Puppy Package Manager. It probably won’t be the case for any Google-Chrome you can install via Puppy Package Manager.
Under Puppies, but maybe not your Puppy. At the present time there are about 30 Puppies, debiandogs and remasters that are actively supported. Each is different, some slightly, some significantly. [At last count, there were over 5,000 Puppies, debiandogs and other operating systems discussed on this and the Old Forum, all of which you can still download and use perhaps with some –perhaps a great deal of-- limitations. On ‘the wrong computer’ one of those might be just the ‘right Puppy.’ We don’t throw anything away]. But here I’m concerned with current applications for one of the ‘30’. An application published for ScPup64 –a Puppy built with Slackware Current 64 binaries-- may not run under BionicPup64-8.0 –a Puppy built with Ubuntu Bionic Beaver 64 binaries; and vice-versa. Know your Puppy: What major Linux distribution is it binary compatible with? If your Puppy is a Remaster, what Puppy was the basis for the remaster? Each Puppy has its own thread. The first few posts in that thread will either provide that information or links to post which will.
Posts on an Application’s Thread will tell you which Puppies they are known to function under; what steps may be necessary; and as importantly, which Puppies they’ll never be able to run under. To quickly obtain access to the information you need to make reasonable decisions there are Search Engines dedicated to Puppy Forums. The Search Box at the Top Right of this Forum’s is OK. But https://rockedge.org/psearch/ is particularly good. Plug in a couple search terms at the same time –for example tahrpup google-- and any relevant posts will be listed with those having all search terms and the newest at the top of the list.
Having done your ‘homework’ you can open Menu>Setup>Puppy Package Manager and type in the name of an application. But don’t click the Auto-Install button yet. Notice that your Puppy offers downloads from its own Repositories, but also the repositories of the distro-version whose binaries were used in your Puppy’s creation. Installing from Puppy’s own repos is safe (usually); but from an ‘alien’ repositiory may not be. See, however, for what to do: Edit Jan 3, 2021. This is a link to a post on the Old forum where I explain how to build applications using PaDS. https://oldforum.puppylinux.com/viewtop ... 6#p1024636 Since that post a new version of PaDS has been published, viewtopic.php?p=6355#p6355. Read the PaDS thread to determine which version to use, then follow the link which details how to build applications.
Don’t forget the most important resource for answering any questions you may have. First do a Search –no reason to wait around for an answer if one has already been posted. But if you still have questions or doubts don’t hesitate to post a question. “A stitch in time saves nine.” There are four logical places for those questions: (1) The thread of a Puppy is where those familiar with that Puppy are likely to know and respond; (2) The thread of an Application –for the same reason; (3) The User’s Section for technical questions; and (4) The Beginner’s Section – for general questions having to do with getting your Puppy up-and-running.
As you examine Application threads for an application there’s a good chance that you’ll find applications available in five* formats: pets, SFSes, AppImages, portables and those which run under Wine. If you have a choice among them, SFSes, AppImages and Portables should be preferred to pets. Pets are installed. SFSes, AppImages and Portables are not. Although constructed differently, those each are like Window’s portable-applications. You don’t have to remove them to test a new version. If they conflict with some other applications, you can simply not run both applications at the same time. And, they may run under whatever upgrade or different Puppy you may later decide on. Regarding Portables, you should be aware that sometimes Applications can be downloaded directly from the web-site of the original publisher –that is before any modifications or packaging by Puppy Devs or Major Distos-- unpacked and run as portables.
During the dozen or so years that Microsoft published Windows XP thousands of programs were published. You’re probably familiar with many, even like some. During much of that time a Group of Linux Devs at WineHQ, https://www.winehq.org/ have been working on a method to run those programs under Linux operating systems. Many Windows programs will run under Wine, including some which were published after Microsoft changed to Windows 7 thru 10. Not all will. You may be able find out if your favorite program is among the ‘can run’ group by using the search box at the top of the cited web-page. But also keep in mind that WineHQ only reports about programs which ‘install’: writing to Windows’ Registry. They don’t report about ‘portable-programs’ such as those you’ll find at https://portableapps.com/apps and elsewhere. My experience is that very often portables will run under Wine; in fact, sometimes the portable version will run even if the ‘installable’ version didn’t. The best thing about portable versions is that if they don’t run you’ve lost nothing more than the time it took to download them, run the setup program, try them and delete their folder.
This is not to suggest that you should run programs under Wine. But I consider it a viable alternative to (a) not having that application at all; (b) spending hours struggling to get the Linux version running; and (c) having multiple versions, one for each of my multiple Puppies.
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* There are two other formats which may be discussed: snaps and flatpaks. These, however, require the installation of applications to even make use of snaps and/or flatpaks packages. There's no guarantee that those applications or that snaps/flatpaks packages themselves will function under your Puppy.