The te-form does not mean anything on its own. It is a connector, and a surprising amount of Japanese grammar is built on top of it.
What it does
Here are the jobs the te-form pulls, all from the same form.
Linking actions
食べて、寝る (tabete, neru): eat, and then sleep. It chains events in order.
Requests
食べてください (tabete kudasai): please eat. The polite way to ask.
Continuous tense
食べている (tabete iru): am eating. Add iru for an ongoing action or a state.
Permission and prohibition
食べてもいい (tabete mo ii): you may eat. 食べてはいけない (tabete wa ikenai): you must not eat.
Forming it
For ichidan verbs, drop る and add て: 食べる becomes 食べて. For godan verbs the ending shifts by sound, which is where the small song many learners memorise comes in: う・つ・る endings become って, む・ぶ・ぬ become んで, and so on. する becomes して, 来る becomes 来て.
nomu to nonde, drink and...
iku to itte, go and... (a common exception)
Practice path
Learn the te-form right after the polite -masu form from the conjugation basics. Once it is automatic, requests and the continuous tense come almost for free.
Test one of these examples in the translator and see how it comes out.
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