When you pull the hood release lever in your vehicle, you are pulling on a cable, just like the brake or shift cables on a bicycle. When the vehicle gets older, and you are under the hood every week to add oil, the cable will eventually wear out and break. So how do you get the hood open without the cable? My experience was with a 1991 Chevrolet S10 Blazer, but the technique I used may be applicable to other vehicles.
The only tools required are a set of pliers, a good work light, and some heavy aluminum wire. The aluminum wire is about twice the thickness of spaghetti, and the stuff I used was 8 gage aluminum ground wire from Radio Shack. The advantage of aluminum is that it is soft enough to work like a string, but stiff enough to create a hook. It also is easily workable with your fingers. If you don't have that, a coat hanger may do.
Set the work light down low so that it shines up through the grill at your latch. In the case of my Blazer, all I could see was the metal casing for the latch. No portion of the mechanism was visible. Here is where a mental picture becomes important. The cable provides a pulling action. You must hook your aluminum wire close to where the cable connects to the mechanism, and then pull in a direction as close to that of the cable as possible. If you don't know what the mechanism looks like, try and find a picture, or find a similar vehicle and examine its mechanism.
In the case of the Blazer, the business end of the cable connects near the front-center part of the case that encloses the mechanism. Make a hook by bending the last 1/4 inch of the wire at a 90 degree angle with the pliers. The aluminum wire can be bent very easily with your bare hands into as many compound angles as needed to make a tool that will reach the end of the mechanism.
It took me about 10 minutes and about four tries pulling to finally hook the mechanism. When you think that you have it, apply some downward pressure to the top of the hood. This will compress the latch spring, and hopefully take some pressure off of the mechanism so that it opens easily. Then, pull steadily on your wire. If you have hooked the mechanism, you will feel it give as the latch operates, and then you can stop pushing down on the hood, and try to lift it up.
Once you get it open, you can replace the latch cable. This can be expensive and time consuming, so if you don't care about how it looks, you can run the aluminum wire out through the grill as a new hood release. In my Blazer, I ran a double length, and then bent it in half at the loop on the mechanism, so I have a double-strength pull. The softness of the aluminum is what allows this to work.
Finally, be sure to grease your latch mechanism well, and also the spring latch on the hood, so that the latch will open as easily as possible. The hood may have rubber leveling feet at each of its corners. If you let these out too far, it will make for a nice, stable hood, but it will put too much pressure on the latch, making it difficult to open, and leading to premature cable failure.