The best way to do this is usually to use the various -exec options to the find command. In particular you should try to use -execdir whenever possible since it runs inside the directory of the file that was found and is generally safer (in the sense of preventing stupid mistakes being disasterous) than other options.
The -exec options are followed by the command you would like to run with {} denoting the spot where the file found by find should be included and are terminated by either \; to run the command once for each file or + to replace {} with a list of arguments of all the matches. Note that the semicolon terminator is escaped so that it is not understood by the shell to be a separator leading to a new command.
Lets say you were finding all text files:
find -iname '*.txt' -execdir rm {} \;
Here is the relevant bit from the find manual (man find):
-exec command ;
Execute command; true if 0 status is returned. All following
arguments to find are taken to be arguments to the command until
an argument consisting of ‘;’ is encountered. The string ‘{}’
is replaced by the current file name being processed everywhere
it occurs in the arguments to the command, not just in arguments
where it is alone, as in some versions of find. Both of these
constructions might need to be escaped (with a ‘\’) or quoted to
protect them from expansion by the shell. See the EXAMPLES sec-
tion for examples of the use of the -exec option. The specified
command is run once for each matched file. The command is exe-
cuted in the starting directory. There are unavoidable secu-
rity problems surrounding use of the -exec action; you should
use the -execdir option instead.
-exec command {} +
This variant of the -exec action runs the specified command on
the selected files, but the command line is built by appending
each selected file name at the end; the total number of invoca-
tions of the command will be much less than the number of
matched files. The command line is built in much the same way
that xargs builds its command lines. Only one instance of ‘{}’
is allowed within the command. The command is executed in the
starting directory.
-execdir command ;
-execdir command {} +
Like -exec, but the specified command is run from the subdirec-
tory containing the matched file, which is not normally the
directory in which you started find. This a much more secure
method for invoking commands, as it avoids race conditions dur-
ing resolution of the paths to the matched files. As with the
-exec action, the ‘+’ form of -execdir will build a command line
to process more than one matched file, but any given invocation
of command will only list files that exist in the same subdirec-
tory. If you use this option, you must ensure that your $PATH
environment variable does not reference ‘.’; otherwise, an
attacker can run any commands they like by leaving an appropri-
ately-named file in a directory in which you will run -execdir.
The same applies to having entries in $PATH which are empty or
which are not absolute directory names.