To be able to “resurrect” an extinct animal you would need some of that animals DNA. For example if we wanted to “resurrect” a dinosaur scientists would need to get hold of some dinosaur DNA so that they could make a clone of it. Back in 2003 it was reported that scientists were able to make a new goat from DNA that they got from an extinct goat, so in theory, it is possible (but very difficult) to “resurrect” extinct animals.
The biggest problem with “resurrecting” extinct animals is not a scientific problem but an ethical (is it right or wrong) problem. Just because you can do something, it doesn’t mean that you should do something. If scientists were to bring back animals that were extinct, like a dinosaur, where would they live? What would they eat? Would it be right to create an animal and make it live in a zoo? These are some of the questions that would need to be answered before scientists try to do this.
Gemma’s answer is great. Just to add a little. There are some scientists who are trying to bring back recently extinct animals. For example the bucardo (a wild goat from south America) was recently attempted to be revived from extinction. However scientists can’t use a machine, we need a closely related species to impregnate with the embryo’s in order for it them to develop.