x0=0;nlast=1000;y0=0;

x[0]=x0;y[0]=y0;
For[n=1,n≤nlast,n++,
q=Random[Integer];
If[q==0,
x[n]=x[n-1]-1,
(*else*)
x[n]=x[n-1]+1;
];(*end if q*)

p=Random[Integer];
If[p==0,
y[n]=y[n-1]-1,
(*else*)
y[n]=y[n-1]+1;
]


](*end for n*)

txy=Table[{x[n],y[n]},{n,0,nlast}];
ListPlot[txy,Joined->True,Mesh->True];
Manipulate[ListPlot[{{x[n],y[n]}},PlotRange->{{-100,100},{-100,100}},PlotStyle->{PointSize->Medium}],{n,0,nlast,1}]