I have already described how to list the contents of specified package using apt-file utility, but you do not need it to check the contents of downloaded package.

I will use rsyslog-pgsq package to show you how to perform different operations.

$ apt-get download  rsyslog-pgsql
Get:1 http://deb.debian.org/debian stretch/main amd64 rsyslog-pgsql amd64 8.24.0-1 [188 kB]
Fetched 188 kB in 0s (7422 kB/s)

Display information about this particular package.

$ dpkg --info rsyslog-pgsql_8.24.0-1_amd64.deb
new debian package, version 2.0.
size 187916 bytes: control archive=1724 bytes.
379 bytes,    18 lines   *  config               #!/bin/sh
498 bytes,    15 lines      control
563 bytes,     7 lines      md5sums
1118 bytes,    43 lines   *  postinst             #!/bin/sh
1459 bytes,    59 lines   *  postrm               #!/bin/sh
124 bytes,    10 lines   *  prerm                #!/bin/sh
Package: rsyslog-pgsql
Source: rsyslog
Version: 8.24.0-1
Architecture: amd64
Maintainer: Michael Biebl <biebl@debian.org>
Installed-Size: 219
Depends: libc6 (>= 2.4), libpq5, debconf (>= 0.5) | debconf-2.0, rsyslog (= 8.24.0-1), dbconfig-common, ucf
Recommends: postgresql-client
Suggests: postgresql
Section: admin
Priority: extra
Homepage: http://www.rsyslog.com/
Description: PostgreSQL output plugin for rsyslog
This plugin allows rsyslog to write syslog messages into a PostgreSQL
database.

Display deb package contents.

$ dpkg --contents rsyslog-pgsql_8.24.0-1_amd64.deb
drwxr-xr-x root/root         0 2017-01-18 22:14 ./
drwxr-xr-x root/root         0 2017-01-18 22:14 ./usr/
drwxr-xr-x root/root         0 2017-01-18 22:14 ./usr/lib/
drwxr-xr-x root/root         0 2017-01-18 22:14 ./usr/lib/x86_64-linux-gnu/
drwxr-xr-x root/root         0 2017-01-18 22:14 ./usr/lib/x86_64-linux-gnu/rsyslog/
-rw-r--r-- root/root     14360 2017-01-18 22:14 ./usr/lib/x86_64-linux-gnu/rsyslog/ompgsql.so
drwxr-xr-x root/root         0 2017-01-18 22:14 ./usr/share/
drwxr-xr-x root/root         0 2017-01-18 22:14 ./usr/share/dbconfig-common/
drwxr-xr-x root/root         0 2017-01-18 22:14 ./usr/share/dbconfig-common/data/
drwxr-xr-x root/root         0 2017-01-18 22:14 ./usr/share/dbconfig-common/data/rsyslog-pgsql/
drwxr-xr-x root/root         0 2017-01-18 22:14 ./usr/share/dbconfig-common/data/rsyslog-pgsql/install/
-rw-r--r-- root/root      1006 2017-01-18 22:14 ./usr/share/dbconfig-common/data/rsyslog-pgsql/install/pgsql
drwxr-xr-x root/root         0 2017-01-18 22:14 ./usr/share/doc/
drwxr-xr-x root/root         0 2017-01-18 22:14 ./usr/share/doc/rsyslog-pgsql/
-rw-r--r-- root/root       438 2017-01-18 22:14 ./usr/share/doc/rsyslog-pgsql/NEWS.Debian.gz
-rw-r--r-- root/root     15362 2017-01-18 22:14 ./usr/share/doc/rsyslog-pgsql/changelog.Debian.gz
-rw-r--r-- root/root    163021 2017-01-10 09:09 ./usr/share/doc/rsyslog-pgsql/changelog.gz
-rw-r--r-- root/root      4454 2017-01-18 22:14 ./usr/share/doc/rsyslog-pgsql/copyright
drwxr-xr-x root/root         0 2017-01-18 22:14 ./usr/share/rsyslog-pgsql/
-rw-r--r-- root/root       152 2017-01-18 22:14 ./usr/share/rsyslog-pgsql/rsyslog-pgsql.conf.template

Simple as that.