By default on mIRC a pop up box will appear on the other person's PC announcing your intention. Diagram 14 shows this.
Diagram 15 shows what the other person would see after accepting the request, whilst Diagram 16 shows what the initiator of the chat would see. Apart from that, a DCC chat operates the same as a query chat.
Another facet of DCC is file transfers. It works in a similar fashion by selecting the receiver's nick and right-clicking. Instead of selecting DCC>Chat, you would use DCC>Send. A dialog box, similar to that shown in Diagram 17 will appear.
From there you can select what file to transfer. Then click Send. On the other end, the person will get a pop-up similar to that of a DCC chat. If they respond a new window is opened on both ends showing a bar graph of the transfer, as well as other details like size and speed (in characters per second). When the transfer is complete the window will close. Note that DCC has a resume function, which means you can continue transfers where you finished if you are cut off.