Initially, you can send a purchase order to your vendor to let them know what you need.
Here's a quick way to generate a purchase order for low or out of stock products:
Highlight the Sales tab.
Select Products and Services.
Tick the boxes of the products you wish to reorder.
Press the Batch actions drop-down menu, then choose Reorder.
It will create a purchase order with the products you selected earlier. At this point, you can edit the contents of this transaction, or add other products you wish to order. Click Save and send when you're done.
When your vendor accepts the purchase order, you can then proceed to convert it to a bill. You can further edit the contents of the bill in case you're receiving partial inventory.
As for paying your vendors via checks, see this article: Enter and pay bills. Follow the steps under the Pay your bills through checks section.