First go to Settings>iCloud on your device and confirm that everything is turned to Off, and that you are not syncing any data with iCloud before proceeding. (If you are, when you delete the data from iCloud it will also be deleted from your device and it will be lost.)
Then go to iCloud.com on your computer, log into your iCloud account and open Contacts, click on the red ribbon at the top to display your groups, click on All Contacts, to the right click on any single contact to select it,click on the Actions (gear shaped) icon at the bottom and choose Select All, then press the Delete key on your keyboard.
For Calendars, open your calendar on icloud.com, click Edit above the calendars list on the left, then tap the minus sign to the right of each calendar to delete it.
For Notes, open your notes on icloud.com, click on each note on the left, then click the trash can icon at the bottom to delete it.
For Reminders, open them on icloud.com, click on each reminder, click on Details to the right, then click on the track can icon to delete it.
For Mail, open your mail on icloud.com, click a folder on the left (such as your inbox), click on a single message to the right, press Control-A on your keyboard to select them all, then click on the trash can icon at the top. Repeat this for each of your mail folders except Trash. When finished, click on the actions (gear-shaped) icon on the upper right and select Empty Trash.