Patches are usually contained in .diff files, because the patches are created using the diff command.
A patch is a series of insertions and deletions into source code. For this reason, in order to use the patch, you must build the application (e.g., "foobar") from source after applying the patch. So, in steps:
1. Get the source package for foobar.
Most linux distributions (n.b. patching is not unique to linux) have "source packages" you can use for this purpose, but since these are heterogeneous, I will only refer to the format of the original source here. The original source is not part of the distro and may be hard to find. A good place to start is wikipedia, which has articles for many popular applications, and the article should contain a link to a homepage with a source download. You can also google yourself, obviously. The source package will be called something like foobar.0.1.tar.bz2. Unpack this -- you now have a directory called foobar.0.1.
2. Add the patch.
Sometimes patches are single files and sometimes they are a set of several files. Copy those into foobar.0.1 and cd foobar.0.1. Next, you need to run the patch command. This reads from standard input, so you want to pipe the .diff file in. The tricky part is determining what to use for the -p option (if there are no instructions with the patch). To do that you need to look at the beginning of the patch file. For example:
--- old/comm.c 2003-09-08 14:25:08.000000000 +0000
+++ new/comm.c 2006-07-07 02:39:24.000000000 +0000
In this case, comm.c is the name of the source file that will be altered. However, notice that there is a directory appended to it. Since these are not the same directory ("old" vs. "new"), this is a big clue that this part of the path is junk (for our purposes). The purpose of the -p switch (see man patch) is to eliminate this prefix. It takes a number, which is the number of slashes (/) to eliminate, with everything in between; in this case we would use -p1 to reduce the path to just plain comm.c.
That presumes comm.c is actually in the same directory, which will be another clue as to whether your interpretation is correct. If both those lines were src/comm.c, and comm.c is actually in the src subdirectory of your build tree, then you need to use -p0 -- beware that not using -p at all will remove ALL slashes. If the path is absolute (i.e., begins with /), that's probably what you want. Now apply the patch:
patch -p1 < patch.diff
The source has now been modified. If there are more .diff files, apply those the same way.
3. Build and install.
This is the normal process you would go through to build something from source -- first ./configure, then make, make check, make install. Before you do the last one, if you already have an existing installation of foobar, decide whether you want to remove or overwrite that or how you are going to deal with the naming conflict. You probably want foobar to refer to your new, patched version, and not the old one.
Best Answer
If you're paying for a support contract, it should be very easy to download the latest Solaris 8 recommended patch bundle from the Oracle Support website and install it using the included script & instructions in that bundle.
Oracle does not make Solaris 8 patches available without paying for a support contract, and is scheduled to stop producing Solaris 8 patches in October 2014 (over 14 years from when the OS was first released in February 2000), but will still charge for access to get existing patches after that date.