LaTeX beamer slideshow presentation

I can't find a feature that allows me to open up a slide to fit the whole screen

Almost any PDF viewer have in the view menu a "Full Screen Mode", "Presentation mode" or something similar,as well as shortcuts as Ctrl+L (Acrobat Reader), F5 (Evince) or Crtl+Shift+P (Okular).Just search in the menu.

But if you want start in this mode to avoid delays in front of the audience, you can use the option pdfpagemode=FullScreen of the hyperref package (already loaded by the document class):

\documentclass{beamer}
\hypersetup{pdfpagemode=FullScreen}
\begin{document}
Hello,World
\end{document}

This way, assuming that you open the PDF with Acrobat Reader (e.g.:acroread file.pdf) it should be showed in the whole screen without Ctrl+L, although this and others viewers as okular will ask for confirmation the first time. Others as xpdf simply ignore this option. Others as evince simply do the job. Others as impressive (really a presentation tool, not a simple pdf viewer) show any PDF in full screen mode, with or without this option.

and then click through my presentation with the space bar.

This is the usual behavior in presentation mode with any PDF viewer (space bar = next page).