In LyX I enter a figure/graphic at the end of a paragraph using Insert > Float > Figure. 
I assume this is the command that I want since I want to include a graphic with a description (please let me know if there's a better command for this).
However, when it shows up in the PDF, (i) the figure is inside the paragraph and (ii) the spacing between the bottom of the figure and the remainder of the paragraph is abnormally large. I've tried manually editing the vertical space, but LyX either puts no space or too much space for this particular figure (I've never had this issue before).
I have a MWE below. In this case the spacing issue no longer appears but the figure appears above the paragraph instead of below. How can I put the figure below the paragraph (or precisely where I want it to appear?
(I) Source Code for Paragraph:
\noindent \begin{center}
\begin{figure}
\includegraphics[scale=0.6]{\string"Thesis/blank billard 7\string".jpg}\caption{A Billiard table $B_{\alpha}$ with a barrier of length $\alpha$}
\end{figure}
\par\end{center}
(II) Source Code for Entire Source:
\documentclass[oneside,english]{amsart}
\usepackage[T1]{fontenc}
\usepackage[latin9]{inputenc}
\usepackage{amsthm}
\usepackage{graphicx}
\usepackage{setspace}
\makeatletter
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Textclass specific LaTeX commands.
\numberwithin{equation}{section}
\numberwithin{figure}{section}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% User specified LaTeX commands.
\title[Short version]{Long version}
\usepackage{mathtools}
\makeatother
\usepackage{babel}
\begin{document}
\subsection{Veech's Examples and a Billiard Interpretation of these Examples}
\begin{doublespace}
\noindent In {[}8{]}, Veech constructs examples of minimal and not uniquely ergodic dynamical systems as follows (see {[}7{]})....
\end{doublespace}
\noindent \begin{center}
\begin{figure}
\includegraphics[scale=0.6]{\string"Thesis/blank billard 7\string".jpg}\caption{A Billiard table $B_{\alpha}$ with a barrier of length $\alpha$}
\end{figure}
\par\end{center}
\end{document}
UPDATE
Here is the figure.
[![enter image description here][2]][2]
Best Answer
Above the float, you should see a box with the text "float: Figure". If you right click it, then select "Settings...", then you should get this box:
Uncheck "Use default placement" and play around with the settings under "Advanced Placement Options". To try David Carlisle's suggestion of htp, select "Here if possible", "Top of page" and "Page of floats".