If you have no puncture repair kit and no tube, there are still ways of riding out. First read up on puncture repair, then think about what items you have to replace the ones listed.
Are there any stickers on your bike which you can peel off and use as a patch on the tube? How about the sticky label on a drink bottle? Do you (for some strange reason) have postage stamps with you? Band-Aids? Any adhesive patch is better than none – even the price sticker on your energy bar may do the trick.
As long as the tube is clean and slightly rough around the puncture, you may have luck getting one of these items to adhere sufficiently to inflate the tire. The trick is to inflate the tube slightly before sticking on the patch, and then to quickly bring it up to pressure inside the tire so that the tire and tube are both pressing on the patch.
Some people have reported success with cutting the ends of the existing flat tube, tying them securely, and then re-inflating. Good luck. My experiments suggest that if you are going to do this, you need to fold the cut ends of the tube back on themselves before tying them off with twine or maybe zip ties. It also helps to put a suitable length loop of twine between the two ends to keep them in a circle.
If your search turns up nothing sticky, you will need a tube replacement. While you can theoretically ride on your rim, this will make it unusable afterwards. Instead, sacrifice the tire. Stuff it really full of pine cones, straw, ferns, leaves, or anything you can find on the trail. Ride slowly as the tire will be likely to roll off the rim. The sidewalls will almost definitely be shot by the end of the ride, but a new tire is typically cheaper and easier to find than a new rim.