After getting into your save, there are 6 buttons at the bottom (appropriately colored).
Green: Home. News gets posted on the whiteboard, which you can shuffle through, blog entries get updated on the Syachi in the upper right corner, and presents get delivered here. Presents come from log-in bonuses and from meeting certain achievements that unlock new member titles. You can only get the latter after restarting your game after meeting the requirements of the achievements.
Blue: Live. A menu appears showing you a list of cities. Tapping on the city will lead to the available missions for that city. Mission titles in red mean that you have to play one specific song while the titles in blue mean that you can pick your own song. A mission at the top of the list will be locked until you complete a certain number of missions on the list. Once it is unlocked, you may complete the mission at the top. Doing so will put a flag down on that town and a new one with a new list of missions will open up. You are free to do any other missions on the list before or after doing the completion mission, and doing all of them will result in a "Perfect Clear" reward of one gold Syachi coin. On the top right of the live screen, you can switch to training mode, which allows you to play any song without any missions attached.
Red: Members. A list, from top to bottom: "Organize Teams," "Power Up," "Skill Up," "Increase Maximum," "Burn Cards," and "Card Box." Organize Teams is where you can make your teams, up to 6. You can also edit your avatar here to add any backgrounds, outfits, or accessories you might have. Backgrounds do not affect your team, but your outfit does have an ability attached. Power Up is where you level your cards up using Syachi Soul that you acquire from burning your cards. Skill Up is where you can level up any special skills your cards might have (only 3 stars and above have skills) with another card of the same type or with Syachi Soul as a gamble. Increase Maximum is where you can increase the maximum level of your card using identical cards. Burn Cards is where you get rid of cards you don't want and Syachi Soul cards to get Soul points. You can burn up to 10 at a time. You can also hit the lower right button to burn the first 10 cards with 2 stars or less to get a slight bonus on the amount of Soul received. Card Box is where you can view your cards.
Yellow: Friends. "Friend List," "User info," "Friend Requests," "Invitation info." You make friends by calling on other users as guests in your shows, which gives you money, and you can confirm them as friends or delete them on this page. Making friends (hitting the leftmost button on your list of pending friends) puts them at the top of your guest list before lives and you automatically earn 100 coins once a day if you bring them to a show. You can also delete friends and see their profile information. User info contains a friend code to send to people, Invitation info is a code to give to new users to give you both a gift, I think? (mine is 1V27d42e)
Pink: Shop and Gacha. "Card Gacha," "Member Gacha," "Videos," "Shop." I explained the card and member gacha above (Card is for cards to use to make teams, member is for your avatar). Videos is where you can buy the solo shots for different songs. Shop is where you can buy premium currency to spend on solo shots or cards or whatever else.
Purple: Other. "Player Details," "Title," "Album," "Member intros," "Oshimen," "Options," "Change player information," "Video Data," "Serial Code," "Move Data," "Support," "Help," "Outside Links," "Return to Title," "Terms of Service," "Privacy Policy," "Credit," "Payment information," "Contact information."