Whats the best way to save a new entry in my plugin? I have a channel section by the name of order. What I need is that every time a user clicks a button on the front end the data of the form is sent to my plugin which then uses the data to create a new entry of type order and saved in the back end. The data in the form only represents the content of the entry and the only other information we have is that the entry is of type channel and that it belongs to the order channel. What would be the best way to create the entry with the publishing date, title, id, etc all set appropriately? Can I use saveEntry of the entries service in some way?
You can use the FrontEnd Entry Form for this. If you want to allow guests (non-registered users) to submit the form, you need to use the Guest Entries plugin.

Both methods will set "publishing date, id, etc" automatically, you just need to specify the title in the form.

If you want to hard-code some field values and prevent the user from changing it, you'd need to create a plugin which checks for entries.onBeforeSaveEntry or guestEntries.beforeSave (if you use Guest Entries plugin).

Edit:

The Entry Form is just an example. You can just as well use an ajax-request to send your data. Just make sure the POST values are set correctly.

If you want to save an entry from within your plugin, use the EntriesService API