As usual, Google is your friend. Take a look at this canonical example which comes out first in my search. The main trick there is using polar coordinates to spread the circles.
If you do not like polar coordinates, add Cartesian coordinates which should make it more convenient to place the numbers and other decorations in an approximation of their "appropriate" positions.
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{shapes,backgrounds}
\begin{document}
\def\firstcircle{(135:1.2) circle (2)}
\def\secondcircle{(45:1.2) circle (2)}
\def\thirdcircle{(-90:1.2) circle (2)}
\begin{tikzpicture}
\tikzset{help lines/.style={color=blue!20}}
\draw[thin,help lines] (-4.5,-4.5) grid (4.5,4.5);
\draw[ultra thin,step=.5,help lines] (-4.5,-4.5) grid (4.5,4.5);
\draw[thick] (-4.5,0) -- (4.5,0); % x acis
\draw[thick] (0,-4) -- (0,4.5); % y acis
\foreach \x in {-4,...,4} { \draw [thick] (\x,0) -- (\x,-0.2); }
\foreach \y in {-4,...,4} { \draw [thick] (0,\y) -- (-0.2,\y); }
\foreach \x in {-4,-3,...,4} { \node [anchor=north,text=blue] at (\x,-0.2) {\x}; }
\foreach \y in {-4,-3,...,4} { \node [anchor=east,text=blue] at (-0.2,\y) {\y}; }
\foreach \x in {-3.5,-3,...,3.5} {\draw [thin,help lines] (\x,0) -- (\x,-0.1);}
\foreach \y in {-3.5,-3,...,3.5} {\draw [thin,help lines] (0,\y) -- (-0.1,\y);}
\draw \firstcircle;
\draw \secondcircle;
\draw \thirdcircle;
\node at (0,0) {2};
\node at (0,1.5) {9};
\node at (1,-0.5) {4};
\node at (-1,-0.5) {5};
\node at (-2,1.5) {10};
\node at (2,1.5) {6};
\node at (2,-3) {
};
\node at (-2,3) {
};
\node at (2,3) {
};
\node at (3,-1) {11};
\node at (-3,-1) {23};
\node at (-3,-3) {13};
\node at (3,3) {13};
\node at (-3,3) {
};
\end{tikzpicture}
\end{document}

Videos
As usual, Google is your friend. Take a look at this canonical example which comes out first in my search. The main trick there is using polar coordinates to spread the circles.
If you do not like polar coordinates, add Cartesian coordinates which should make it more convenient to place the numbers and other decorations in an approximation of their "appropriate" positions.
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{shapes,backgrounds}
\begin{document}
\def\firstcircle{(135:1.2) circle (2)}
\def\secondcircle{(45:1.2) circle (2)}
\def\thirdcircle{(-90:1.2) circle (2)}
\begin{tikzpicture}
\tikzset{help lines/.style={color=blue!20}}
\draw[thin,help lines] (-4.5,-4.5) grid (4.5,4.5);
\draw[ultra thin,step=.5,help lines] (-4.5,-4.5) grid (4.5,4.5);
\draw[thick] (-4.5,0) -- (4.5,0); % x acis
\draw[thick] (0,-4) -- (0,4.5); % y acis
\foreach \x in {-4,...,4} { \draw [thick] (\x,0) -- (\x,-0.2); }
\foreach \y in {-4,...,4} { \draw [thick] (0,\y) -- (-0.2,\y); }
\foreach \x in {-4,-3,...,4} { \node [anchor=north,text=blue] at (\x,-0.2) {\x}; }
\foreach \y in {-4,-3,...,4} { \node [anchor=east,text=blue] at (-0.2,\y) {\y}; }
\foreach \x in {-3.5,-3,...,3.5} {\draw [thin,help lines] (\x,0) -- (\x,-0.1);}
\foreach \y in {-3.5,-3,...,3.5} {\draw [thin,help lines] (0,\y) -- (-0.1,\y);}
\draw \firstcircle;
\draw \secondcircle;
\draw \thirdcircle;
\node at (0,0) {2};
\node at (0,1.5) {9};
\node at (1,-0.5) {4};
\node at (-1,-0.5) {5};
\node at (-2,1.5) {10};
\node at (2,1.5) {6};
\node at (2,-3) {
};
\node at (-2,3) {
};
\node at (2,3) {
};
\node at (3,-1) {11};
\node at (-3,-1) {23};
\node at (-3,-3) {13};
\node at (3,3) {13};
\node at (-3,3) {
};
\end{tikzpicture}
\end{document}

\documentclass[border=2mm,tikz]{standalone}
\usepackage{bm}
\begin{document}
\begin{tikzpicture}[thick]
\draw (2.7,-2.54) rectangle (-1.5,1.5) node[below right] {$\bm{U}$};
\draw (0,0) circle (1) node[above,shift={(0,1)}] {$\bm{M}$};
\draw (1.2,0) circle (1) node[above,shift={(0,1)}] {$\bm{N}$};
\draw (.6,-1.04) circle (1) node[shift={(1.1,-.6)}] {$\bm{L}$};
\node at (.6,-.4) {2};
\node at (1.2,-.7) {4};
\node at (0,-.7) {5};
\node at (1.4,.2) {6};
\node at (.6,.3) {9};
\node at (-.2,.2) {10};
\node at (2.2,-1.2) {11};
\node at (-1,-2.2) {12};
\node at (2.4,1.2) {13};
\node at (.3,-1.5) {16};
\node at (1,-1.4) {21};
\node at (-1.2,-1.5) {23};
\end{tikzpicture}
\end{document}

Use polar coordinates.
\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\def\firstcircle {(210:1.1cm) circle (1.5cm)}
\def\secondcircle{(330:1.1cm) circle (1.5cm)}
\def\thirdcircle {( 90:1.1cm) circle (1.5cm)}
\colorlet{circle edge}{red!50}
\colorlet{circle area}{red!20}
\tikzset{filled/.style={fill=circle area, draw=circle edge, thick},
outline/.style={draw=circle edge, thick}}
\setlength{\parskip}{5mm}
\begin{scope}
\clip \secondcircle;
\fill[filled] \thirdcircle;
\end{scope}
\begin{scope}
\clip \firstcircle;
\fill[filled] \thirdcircle;
\end{scope}
\draw[outline] \firstcircle node {$M_1$};
\draw[outline] \secondcircle node {$M_2$};
\draw[outline] \thirdcircle node {$M_3$};
\node[anchor=south] at (current bounding box.north) {$M_1 \cap M_2 \cap M_3$};
\end{tikzpicture}
\end{document}

(Note that the expression above your drawing does not fit the shaded area in the drawing.)
In this Asymptote solution
we create a set of the key points first,
then using them
as the centers of the circles
and corresponding begin-end points of the circular arcs,
we construct an addressable list
of the area boundaries, so
each area can be filled differently.
The color used for the intersecting region is chosen as an average of the colors of corresponding intersecting regions.
The named points are shown for convenience.
//
// Venn-diag.asy
//
// run
// asy Venn-diag.asy
//
// to get a standalone Venn-diag.pdf
//
settings.tex="pdflatex";
size(7cm);
import fontsize;defaultpen(fontsize(8pt));
texpreamble("\usepackage{lmodern}"+"\usepackage{amsmath}"
+"\usepackage{amsfonts}"+"\usepackage{amssymb}");
pair A,B,C,D,E,F,O;
transform t=rotate(120);
O=0; A=(0,-1/sqrt(3));
B=t*A; C=t*B;
D=A-1; E=A+1; F=2B-E;
guide[] g={arc(A,D,E)&arc(B,E,A,CW)&arc(C,A,D,CW)&cycle,};
g.cyclic=true;
g.push(t*g[-1]);
g.push(t*g[-1]);
g.push(arc(B,A,E)&arc(A,E,B)&arc(C,B,A,CW)&cycle);
g.push(t*g[-1]);
g.push(t*g[-1]);
g.push(arc(C,A,B)&arc(A,B,C)&arc(B,C,A)&cycle);
pen[] fPen={lightred,deepgreen,lightblue,};
fPen.push(0.5*(fPen[0]+fPen[1]));
fPen.push(0.5*(fPen[1]+fPen[2]));
fPen.push(0.5*(fPen[2]+fPen[0]));
fPen.push(1/3*(fPen[0]+fPen[1]+fPen[2]));
for(int i=0;i<fPen.length;++i) fill(g[i],fPen[i]);
draw(circle(A,1),red+.7*bp);
draw(circle(B,1),deepgreen+.7*bp);
draw(circle(C,1),blue+.7*bp);
string[] s=array("ABCDEF");
pair[] p={A,B,C,D,E,F,};
dot(p,UnFill);
for(int i=0;i<p.length;++i) label("$"+s[i]+"$",p[i],dir(p[i]));
pair L=A-(0,1/2);
for(int i=0;i<3;++i)label("$\mathbf M_"+string(i+1)+"$",t^i*L,white);
L=(A+B+E)/3*1.2;
label("$M_1\cap M_2$",L,white);
label("$M_2\cap M_3$",t*L,white);
label("$M_1\cap M_3$",t^2*L,white);
label("$M_1\cap M_2\cap M_3$",white);
