Figure in LaTeX

\usepackage{graphicx}

With pdflatex, graphicx accepts PNG, JPG and PDF files. Charts are best saved as PDF: they stay sharp at any zoom level. The file extension in \includegraphics can be left out.

\begin{figure}[h]
  \centering
  \includegraphics[width=0.7\textwidth]{chart.png}
  \caption{Period as a function of pendulum length}
  \label{fig:chart}
\end{figure}

[h] asks LaTeX to place the figure here, but it is a request, not an order: when there is not enough room, the figure moves to the next page. \centering inside the environment avoids the extra vertical space the center environment would add.

\usepackage{float}
% ...
\begin{figure}[H]
  \centering
  \includegraphics[width=0.7\textwidth]{chart.png}
  \caption{Period T against length L}
\end{figure}

The capital H from the float package puts the figure exactly where it is in the source, so in a lab report the chart stays right under the description of the measurement. The price can be empty space at the bottom of the previous page.

\usepackage{subcaption}
% ...
\begin{figure}[h]
  \centering
  \begin{subfigure}{0.48\textwidth}
    \includegraphics[width=\linewidth]{series1.png}
    \caption{First series}
  \end{subfigure}\hfill
  \begin{subfigure}{0.48\textwidth}
    \includegraphics[width=\linewidth]{series2.png}
    \caption{Second series}
  \end{subfigure}
  \caption{Comparison of the measurement series}
\end{figure}

Each subfigure gets a letter, (a) and (b), and the whole group shares one number. Inside a subfigure \linewidth is the width of that column, not of the page, and \hfill pushes the two images to the edges.

\graphicspath{{figures/}}

When images live in a subfolder, declare it once in the preamble and use bare file names afterwards. The trailing slash is required, and the double braces are not a typo: you can list several folders, each in its own pair.

\includegraphics[width=0.5\textwidth, angle=90]{diagram.png}
\includegraphics[trim=1cm 0 1cm 0, clip, width=0.6\textwidth]{photo.jpg}

angle rotates the image by the given number of degrees. trim cuts the margins in the order left, bottom, right, top, and clip hides the trimmed parts, so a photo of the setup can be fixed without an image editor.