Go into the 'people' app. There are 3 tabs on the top. The left tab is the groups. You can add a new group by pressing the little icon at the bottom that looks like people with a + sign. Once you've created your groups, go to the middle tab. This should be your contacts. You can now go into each contact and choose 'edit'. In the contact edit page there is a selection labeled 'groups'. You can click on that and then select which of your groups that contact is in. When you are done, save the contact and move to the next one.
Alternatively, if you'd like to add contacts in bulk instead of one by one, you can do it in the browser. Log in to gmail, click on 'gmail V' in the upper left and choose 'contacts'. Once in contacts, you can select 'new group' towards the bottom of the left column, and create your groups. You can then go to 'my contacts' and put a checkmark next to multiple contacts, then choose the icon at the top that looks like 3 people with an arrow next to it. Then you can choose which group the selected contacts should be in. You can then repeat for each group.
