Remember Forrest Gump? "Shrimpin' is
HARD." Well, when it comes to low/no/mini/micro budget filmmaking, in fact, when it comes to filmmaking in general,
"production sound is HARD!" Without a budget you have extremely limited options, and all of them are either restrictive, extremely difficult, or both.
Good production sound relies on getting a mic in close and properly aimed.
The Inverse Square Law - In physics, an inverse-square law is any physical law stating that a specified physical quantity or intensity is inversely proportional to the square of the distance from the source of that physical quantity.
So if you hold the mic two (2) inches from the sound source it will only be one quarter (1/4) as loud than if you held the mic one (1) inch away from the sound source. If you are four (4) inches away it will only be one sixteenth (1/16) as loud than if you held the mic one (1) inch away from the sound source. If you hold the mic eight (

inches from the sound source it will only be one sixty-fourth (1/64) as loud.
And all of that is if the situation is optimal, meaning that the mic is properly aimed. If the mic is not exactly aimed you will be recording more noise and less dialog.
Since you have no external mic, that means getting the camera mic in extremely close, which, of course, is very restrictive of the type of shots you probably want to get. If you opt to get all the shots that you want you're going to end up with very noisy production sound. Cleaning up cluttered, noisy production sound is a hard job even for well equipped experienced audio post types.
So, as has been mentioned, the only solution is ADR (Automated Dialog Replacement). ADR requires the actors to go into a studio (which you can't afford) to perform their lines while EXACTLY matching the lip movements on the screen. This is difficult to achieve, especially if you don't have access to tools like VocAlign. On top of that, your actors still need to give emotional performances. To match sync and at the same time give an emotional performance is a difficult task even for high-paid experienced actors, much less inexperienced actors.
Oh, by the way, when you do ADR you will also have to do Foley to replace all of the human-made sounds like footsteps, cloth, small props, kissing, punching, etc. You will also have to replace the ambient background sounds and do sound effects to replace all visible audio cues (vehicles, doors, etc.).
Without having any knowledge as to what audio resources are available to you it is nearly impossible to advise you. Hopefully your media center will cooperate.
I wish you luck.