To delete some parts of a document you can of course select them, and then use the Delete key. Kate also offers the command Ctrl-K which deletes the hole line.But Kile offers a faster way with its own delete commands. Under Edit->Delete you will find following commands to delete text.

Edit->Delete items
Environment (inside) (Ctrl+Alt+TE)

Delete an environment without the surrounding tags.

Environment (outside) (Ctrl+Alt+TF)

Delete an environment including the surrounding tags.

TeX Group (inside) (Ctrl+Alt+TT)

Delete a TeX group inside the surrounding braces.

TeX Group (outside) (Ctrl+Alt+TU)

Delete a TeX group including the surrounding braces.

Math Group (Ctrl+Alt+TM)

Delete the current math group including the math commands.

Paragraph (Ctrl+Alt+TP)

Delete a whole paragraph. Look at the Select->Paragraph command, how a paragraph is defined in Kile.

To End of Line (Ctrl+Alt+TI)

Delete the text from the current cursor position to the end of the line.

TeX Word (Ctrl+Alt+TW)

Delete the word or LATEX command under the current cursor position.