I am using latex for first time. I want to draw the picture below. How to proceed?

Something like this:

The main idea is to use tikz polar coordinates and a loop:

documentclassarticle
usepackagetikz

begindocument

 begintikzpicture[bullet/.style=circle, fill, inner sep=2pt]
 foreach lab [count=c, 
 evaluate=c as ang using 18+72*c] 
 in a,b^2, ab^2, ab, b 
 node[bullet] (c) at (ang:10mm) ;
 node at (ang:14mm)$lab$;
 foreach i in 1,...,c 
 draw(i)--(c);
 
 
 endtikzpicture

enddocument

EDIT
Oops, I noticed that I have an extra edge. If this really is not wanted then here is a fix to give:

using:

documentclassarticle
usepackagetikz

begindocument

 begintikzpicture[bullet/.style=circle, fill, inner sep=2pt]
 foreach lab [count=c, evaluate=c as ang using 18+72*c] in a,b^2, ab^2, ab, b 
 node[bullet] (c) at (ang:10mm) ;
 node at (ang:14mm)$lab$;
 
 draw(5)--(1)--(2)--(3)--(4)--(5)--(3)--(1)--(4)--(2);
 endtikzpicture

enddocument

Without additional packages:

documentclassarticle

begindocument

beginpicture(100,100)
put(50,100)circle*5
put(98,65)circle*5
put(79,10)circle*5
put(21,10)circle*5
put(2,65)circle*5

put(48,105)$a$
put(103,65)$b$
put(84,10)$ab$
put(0,10)$ab^2$
put(-10,65)$b^2$

qbezier(79,10)(79,10)(21,10)
qbezier(79,10)(79,10)(98,65)
qbezier(79,10)(79,10)(50,100)
qbezier(21,10)(21,10)(98,65)
qbezier(21,10)(21,10)(50,100)
qbezier(21,10)(21,10)(2,65)
qbezier(2,65)(2,65)(50,100)
%qbezier(2,65)(2,65)(98,65)
qbezier(2,65)(2,65)(79,10)
qbezier(50,100)(50,100)(98,65)

endpicture

enddocument

Asymptote

Based on https://tex.stackexchange.com/a/152591/189040

documentclassarticle
usepackageasymptote
begindocument
beginasy
size(3cm,0); 
pair[] vertices;
int n = 5; 
real r = 1.0; 

// Add the vertices to the array:
for (real angle = 18; angle < 378; angle += 360/n) 
 // The `push` command adds its argument to the end of the array.
 vertices.push(r*dir(angle)); // r*dir(angle) gives the point with polar coordinates (r, angle).


// Draw the vertices:
for (pair vertex : vertices)
 dot(vertex);

// Draw a couple lines in respective:
draw(vertices[0] -- vertices[1], black);
//draw(vertices[0] -- vertices[2], black);
draw(vertices[0] -- vertices[3], black);
draw(vertices[0] -- vertices[4], black);

draw(vertices[1] -- vertices[2], black);
draw(vertices[1] -- vertices[3], black);
draw(vertices[1] -- vertices[4], black);

draw(vertices[2] -- vertices[3], black);
draw(vertices[2] -- vertices[4], black);

draw(vertices[3] -- vertices[4], black);

label("b", vertices[0], align=E);
label("a", vertices[1], align=N);
label("$b^2$", vertices[2], align=W);
label("$ab^2$", vertices[3], align=SW);
label("ab", vertices[4], align=SE);

endasy
enddocument

PSTricks

Based on https://tex.stackexchange.com/a/228371/189040

documentclassarticle

usepackagepst-node,multido

begindocument

beginpspicture(5,5)
 multidoi=0+17rput90degrees[5]pnode(1;i)vi% Mark nodes
 multidoi=0+15%
 pcline(vi)(vnumbernumexpri+1)% C_5<1>
 pscircle[fillstyle=solid,fillcolor=black](vi)2pt% node
 
 multidoi=0+14%
 pcline(vi)(vnumbernumexpri+2)% C_5<2>
 


uput[90](v0)a 
uput[180](v1)$b^2$ 
uput[180](v2)$ab^2$ 
uput[0](v3)$ab$ 
uput[0](v4)$b$ 

endpspicture

enddocument

Or using shapes.geometric.

documentclass[tikz,border=3.14mm]standalone
usetikzlibraryshapes.geometric
begindocument
begintikzpicture
 defLstG"","a","b^2","ab^2","ab","b"
 node[regular polygon,regular polygon sides=5,draw,minimum width=8em] (5gon);
 draw (5gon.corner 2) node[circle,fill,inner
 sep=1.5pt,label=18+72*2:pgfmathsetmacrolblLstG[2]$lbl$] 
 foreach X in 4,1,3,5 -- (5gon.corner X)
 node[circle,fill,inner
 sep=1.5pt,label=18+72*X:pgfmathsetmacrolblLstG[X]$lbl$];
endtikzpicture
enddocument

Maybe, this can help you.

documentclass[tikz]standalone

begindocument
 begintikzpicture
 draw[ultra thin] (0,0)--(3.5,-2.2)--(2.7,-6)--(-2.7,-6)--(-3.5,-2.2)--(0,0)--
 (2.7,-6)--(-3.5,-2.2);
 draw[ultra thin] (0,0)--(-2.7,-6)--(3.5,-2.2);
 draw [fill](0,0)circle[radius=0.7mm]node[above]$a$;
 draw [fill](3.5,-2.2)circle[radius=0.7mm]node[right]$b$;
 draw [fill](2.7,-6)circle[radius=0.7mm]node[below]$ab$;
 draw [fill](-2.7,-6)circle[radius=0.7mm]node[below]$ab^2$;
 draw [fill](-3.5,-2.2)circle[radius=0.7mm]node[left]$b^2$;
 endtikzpicture
enddocument

A PSTricks solution only for fun purposes. It was intentionally or deliberately made complicated to popularize the buried features in PSTricks such as:

• degrees


• saveNodeCoors


• curvepnodes


• psnpolygon


• PtoCrel


• DegtoAny

documentclass[pstricks,12pt]standalone
usepackagepst-plot
degrees[5]
begindocument
beginpspicture[saveNodeCoors](-5,-5)(5,5)
 curvepnodes[plotpoints=6]054 t 1 4 div add PtoCrelA
 psnpolygon[showpoints,dotscale=2](0,Anodecount)A
 foreach i/j in 0/b,1/a,2/b^2,3/ab^2,4/ab
 uput10pt[!N-Ai.y N-Ai.x atan DegtoAny](Ai)$j$
 foreach i/j in 3/0,3/1,4/1,4/2
 pcline(Ai)(Aj)
endpspicture
enddocument