You will need your title number and the date of the lease, do you have that? If not then it may be a little more complicated.
Ignore the references to a key number and DX, these relate to conveyancers, legal advisors.
The nature of the document will be the type of document, eg Lease.
Section 7 has two parts as not all documents are noted on the title register held at the Land Registry. As a Lease is a fundamental title document, I anticipate it is on the title, especially as you have had a copy, albeit mislaid it.
These should help make general sense of the document but it there are bits you still don't understand then let me know.
Fees wise, they are here:
http://www.landregistry.gov.uk/__data/assets/pdf_file/0007/18628/information-services-fees-2012.pdf
See OC2 for a copy of a lease - £23.
You will also need to know which Land Registry to send it to, do you know that? If not, do you have a copy of your title register which should tell you. There have been some changes over the years but you can double-check with the Land Registry, just ring your local one or the one you think it is and ask.