For a beginning piano student learning to play legato and staccato can be very challenging. When singing, it is possible to sing true legato, but on a piano it is harder. This is because you have to physically press a new key but create the illusion that the sound is continuos. Staccato is also challenging because our temptation is to hit the key with brute force. This is NOT staccato! When playing staccato each finger should stay near the key and push up, rather than dropping from high and rebounding.
Of course, when learning any new concept, demonstration is better that a written exercise. I found a helpful piano tutorial on legato and staccato from Piano-Play-It.com. This is a great demonstration of what legato and staccato should look like. It also mentions legatissimo and staccatissimo which are two other touches to know. For the purposes of beginners though, legato and staccato would be the ones to learn first.
You can also see the piano tutorial down below: