With Jumi you can develop your own modules and plugins very quickly and easily. See how to do that.
For the beginning I greatly recommend you to study demos and code snippets that are downloadable from this site at the least.
After you have finished tests of your custom code you are recommended to add several lines at the very beginning of your code
NEVER forget to start your Joomla! php code with following lines! Never! They are very important for security reasons!
They prevent opening the php code directly bypassing the Joomla! environment.
The "security" lines introduced above work in both Joomla! 1.0.x and 1.5.x.
After you had developed your script application you have to upload it to your site. Then you can just include it into your Jumi module (published in any position) or Jumi plugin (in the content).
Really, it's easy.
Your environment: Joomla! and PHP
Do not forget that your scripts are "living" in Joomla! and PHP environment. So you have full access to global and superglobal variables and Joomla objects and methods.
I greatly recommend using Joomla! API whenever possible. It can save you a great deal of work!