My apologies for having missed the questions that you posted here.
A button can be associated with a script step or a script by choosing either option from the Action drop-down in the Button Setup dialog.
For now let's keep it simple and choose "Single Step".
This causes a Button Action dialog window to appear.
In the space where it says "Type a step or choose from the list" type: Send Mail
This causes the Send Mail script step to appear in a drop down. Select it.
The Send Mail script step is selected. Now you need to configure its settings. Click on the gear icon that appears next to the script step name.
For now, leave the "Perform without dialog" checkbox unchecked. This allows you to see the email that will be generated before it is sent.
Click the Specify... button.
A "Send Mail" Options dialog window appears.
Enter values as appropriate in the various fields. You can enter actual email addresses as aa single string enclosed in quotes (with multiple addresses separated by commas), or you can write a calculation formula that generates one or more email addresses separated by commas.
For now, keep the 'Send via:" option as "E-Mail Client". This means that the default email application on your computer will be used.
Hope this gets you started!