Present tense verbs form the basis of every verb. Use the present tense to refer to an action you are doing right now. "They walk," from the Purdue University example, is a complete sentence in the present tense. This is the present tense in its most basic form. You can build up and use different forms of present tense verbs to describe longer events, but all English verbs start with the simple present tense. Use the present tense to talk about things you are doing today.
The past tense refers things that happened any time before now. Even if something occurred just a few seconds ago, you need to use past tense to talk about it. Consider: "They walked." This is the past tense of "walk." But past-tense can be tricky to learn, especially because a lot of past-tense verbs don't follow an easy rule. For instance, some verbs in the past tense have an "ed" ending, while others -- called irregular verbs -- have a special form for the past tense. This is why a young child might say "I goed to the park" instead "I went to the park." Use the past tense to talk about thing you did yesterday.
The future tense talks about things that will happen after now. Consider "They will walk." This means that the subject didn't walk and isn't walking now, but that he will walk in the future. Most future tense sentences use "will" or "going to." Use the future tense to talk about something you will do tomorrow.
The approaches to teaching verb tense change depending on the learners. You won't teach a young child and an adult learning English for the first time the same way, for example, but can use the same basic philosophy. Keep things simple. Explain new verbs in terms of yesterday, today, and tomorrow (then expanding to the distant past and future) and give an example of each tense. When a student or child makes a mistake, correct them gently by saying the right phrase. When your nephew says "goed to the park," just repeat the correct verb in a question, like "You went to the park? What did you do?" Once students have the basics down -- past, present and future -- you can build and start to use the past, present and future continuous and perfect forms.