You could write a LinuxDoc document without having any LinuxDoc software. However, it's likely that it would contain some errors in the tags (or their use) so that it would be returned to you for correction. Even if there were no errors, the results might not not look quite right. So it's best for you to have the software to convert your source code on your computer.
The Debian distribution of Linux has a linuxdoc-tools package. There is also a rpm package for non-Debian distributions. It was formerly called sgml-tools. Don't use the sgmltools-2 package which is primarily for DocBook-sgml.
To use linuxdoc-tools you run converter programs on the *.sgml files. For example for versions after 0.9.21-0.8 to get text output, type: "sgml2txt -f --blanks=1 my-HOWTO.sgml". For earlier versions due to a bug you must substitute --pass="-P-cbou" for -f. (If interested, see Old Problem of Escape Sequences in Text Output for more info on this bug.) To get html output,type: "sgml2html my-HOWTO.sgml". If it shows errors, it will show the line number and the column number where the error is in the source file. Typing "man -k sgml" should show you a number of other programs with a one-line description of each but not all of them are for linuxdoc-sgml.