package My::App;
use base 'CGI::Application';
use DBI;
#...

sub _connect
{
  my $self = shift;
  my $dbh = $self->param('dbh');
  return $dbh if $dbh;

  my $dsn = $self->param('dsn');
  # user, password...
  $dbh = DBI->connect($dsn, ...);
  $self->param('dbh' => $dbh);
  $dbh;
}

sub _prepare
{
  my $self = shift;
  my $dbh  = $self->_connect();
  $dbh->prepare(@_);
}

sub _execute
{
  my $self = shift;
  my $sth  = shift;
  $self->{_execute}++; # here it is...
  $sth->execute(@_);
}