Unlike other editors, Vim stores copied text in its own clipboard. So, it's very hard for me to copy some text from a webpage and paste it into the current working file. It so happens I have to either open gedit or type it manually.
Can I make Vim paste from (and copy to) the system's clipboard?
Try using "*yy or "+yy to copy a line to your system's clipboard.
Be aware that copying/pasting from the system clipboard will not work if :echo has('clipboard') returns 0. In this case, Vim is not compiled with the +clipboard feature and you'll have to install a different version or recompile it. Some Linux distros supply a minimal Vim installation by default, but if you install the vim-gtk or vim-gtk3 package you can get the extra features nonetheless.
The "* and "+ registers are for the system's clipboard (:help registers). Depending on your system, they may do different things. For instance, on systems that don't use X11 like OS X or Windows, the "* register is used to read from and write to the system clipboard. On X11 systems, both registers can be used. See :help x11-selection for more details, but basically the "* is analogous to X11's _PRIMARY_ selection (which usually copies things you select with the mouse and pastes with the middle mouse button) and "+ is analogous to X11's _CLIPBOARD_ selection (which is the clipboard proper).
If all that went over your head, try using "*yy or "+yy to copy a line to your system's clipboard. Assuming you have the appropriate compile options, one or the other should work.
You might like to remap this to something more convenient for you. For example, you could put vnoremap <C-c> "*y in your ~/.vimrc so that you can visually select and press Ctrl+c to yank to your system's clipboard.
You also may want to have a look at the 'clipboard' option described in :help cb. In this case, you can :set clipboard=unnamed or :set clipboard=unnamedplus to make all yanking/deleting operations automatically copy to the system clipboard. This could be an inconvenience in some cases where you are storing something else in the clipboard as it will overwrite it.
To paste you can use "+p or "*p (again, depending on your system and/or desired selection) or you can map these to something else. I type them explicitly, but I often find myself in insert mode. If you're in insert mode you can still paste them with proper indentation by using <C-r><C-p>* or <C-r><C-p>+. See :help i_CTRL-R_CTRL-P.
Vim's paste option (:help paste) is also worth mentioning: This puts Vim into a special "paste mode" that disables several other options, allowing you to easily paste into Vim using your terminal emulator's or multiplexer's familiar paste shortcut. (Simply type :set paste to enable it, paste your content and then type :set nopaste to disable it.) Alternatively, you can use the pastetoggle option to set a keycode that toggles the mode (:help pastetoggle).
I recommend using registers instead of these options, but if they are still too scary, this can be a convenient workaround while you're perfecting your Vim chops.
See :help clipboard for more detailed information.