Ok, so here's a step-by-step guide to what I ended up doing. The answers were helpful, but none of them really provided the information I needed as a newbie to get it up and running.
1) Download and Install Sonatype Nexus on a machine connected to the internet
2) Install another version of Sonatype Nexus on the offline development network
3) Create an 'empty' Maven project in Eclipse
4) Add the following to $USER_HOME\.m2\settings.xml
(the location of this folder is specified in Eclipse in Preferences->Maven->User Settings)
<settings>
...
<mirrors>
<mirror>
<id>central-nexus</id>
<name>Central (Nexus)</name>
<url>http://localhost:8081/nexus/content/repositories/central/</url>
<mirrorOf>central</mirrorOf>
</mirror>
</mirrors>
...
</settings>
5) Add required dependencies to the pom.xml
- e.g. (The brackets around the version number will tell it to download newer versions too.)
<dependency>
<groupId>org.apache.tika</groupId>
<artifactId>tika-parsers</artifactId>
<version>[1.5,)</version>
</dependency>
6) Compile the project. This will cause Nexus to cache all the JARs and their dependencies.
7) Transfer the $NEXUS_ROOT\sonatype-work\nexus\storage
folder to the offline network and replace the files in there with the copied files
I haven't yet worked out if there's a smarter way to do the copying so only the updates are copied, but it's got me started at least.
Thanks for the pointers in the right direction, and hopefully these instructions will be clear enough for other Maven newbies to follow.