The first thing to do is identify the missing libraries. You may have already done this, but what I do is locate each of the application's binaries. There's usually only one, and the application's /usr/share/application/...desktop file's argument (Exec=) will either identify it, or a wrapper (bash-script you can open in a text editor and look for name of the actual binary). When you Menu>filesystem>pfind, then file-browse to that binary, look nearby for similarly named binaries: e.g. my-application, my-application-more.
Right-Click all binaries and select ListDD from the pop-up menu. At the bottom of ListDD's GUI, click the "missing tab".
If it reports that glibc newer than that used by your Puppy is missing Quit. [It may be possible to construct an application that will internally contain a newer glibc --ala palemoon-with-glib-tweak-- but you really need to know what your doing; and even then it won't always work].
Now that ListDD has listed all the missing dynamic libraries, copy each list to a text file.
Open you web-browser to https://pkgs.org/. At the top-right is a search box. You can copy & paste each of the names of the missing dependencies into it. But use a little imagination. For example, if libgobject-2.0.so.0 was the missing file, have pkgs.org search for libgobject-2.0, and if nothing is found, try libgobject, then just gobject.
Know which major distro AND version with which your Puppy is binary-compatible. pkgs.org search will provide links to the repositories of AFAIK all the major Linuxes, and several minor. Your search may, for example, reveal that packages are available for slackware 14.1, slackware 14.2, and slackware current. Or none for slackware, but some for debian 9.
A package --such as a pet-- consists of files organized in such a way that the package-manager of the distro they are created to use in will properly install each file into that distro's file structure. UExtract can decompress almost all package enabling you to then manually copy the extracted files into a proper location for a Puppy to make use of it.
But there are two 'got-yas'.
The first is the files within a package were compiled to work under the Distro and version they were compiled in. In order to use a library in a different Distro-Version you may have to (a) also install other libraries; and libraries those libraries depend on. And you may have to create symbolic links. For example, your application is looking for libgobject-2.0.so.0 but the closest file you could find was libgobject-2.0.so.14. You could create a symbolic link named libgobject-2.0.so.0 pointing to libgobject-2.0.so.14.
The second 'got-ya' is that while a file compiled for one distro-version may be identical to that of a different distro-version (the difference between the packages being only how they were packaged) sometimes they are not.
The further you depart from the libraries compiled for your Puppy-binary-compatible distro the less likely you will be able to find a workaround.