I normally use rdepends for that, install it with sudo apt-get install apt-rdepends or look for in the Ubuntu Software Center.
After installing the program you can use it simply by opening a terminal and typing sudo apt-rdepends <package_name>.
It will show you all the dependencies any package that is in your apt lists required to install and all the dependencies of a package that you might be thinking about installing.
It shows the information in a tree diagram where all the dependencies from one package are compared against all the dependencies of the each package dependency... (and so).
ie:
sudo apt-rdepends sqlite
Reading package lists... Done
Building dependency tree
Reading state information... Done
sqlite3
Depends: libc6 (>= 2.4)
Depends: libreadline6 (>= 6.0)
Depends: libsqlite3-0 (>= 3.6.18)
libc6
Depends: libc-bin (= 2.13-20ubuntu5)
Depends: libgcc1
Depends: tzdata
libc-bin
libgcc1
Depends: gcc-4.6-base (= 4.6.1-9ubuntu3)
Depends: libc6 (>= 2.2.4)
PreDepends: multiarch-support
gcc-4.6-base
multiarch-support
Depends: libc6 (>= 2.13-0ubuntu6)
tzdata
Depends: debconf (>= 0.5)
Depends: debconf-2.0
debconf
PreDepends: perl-base (>= 5.6.1-4)
perl-base
PreDepends: dpkg (>= 1.14.20)
PreDepends: libc6 (>= 2.11)
dpkg
PreDepends: coreutils (>= 5.93-1)
PreDepends: libbz2-1.0
PreDepends: libc6 (>= 2.11)
PreDepends: libselinux1 (>= 1.32)
PreDepends: xz-utils
PreDepends: zlib1g (>= 1:1.1.4)
coreutils
PreDepends: libacl1 (>= 2.2.11-1)
PreDepends: libattr1 (>= 2.4.41-1)
PreDepends: libc6 (>= 2.7)
PreDepends: libselinux1 (>= 1.32)
libacl1
Depends: libattr1 (>= 2.4.41-1)
Depends: libc6 (>= 2.4)
PreDepends: multiarch-support
libattr1
Depends: libc6 (>= 2.4)
PreDepends: multiarch-support
libselinux1
Depends: libc6 (>= 2.8)
PreDepends: multiarch-support
libbz2-1.0
Depends: libc6 (>= 2.4)
xz-utils
Depends: libc6 (>= 2.7)
Depends: liblzma2 (>= 5.0.0)
liblzma2
Depends: libc6 (>= 2.4)
zlib1g
Depends: libc6 (>= 2.4)
PreDepends: multiarch-support
debconf-2.0
libreadline6
Depends: libc6 (>= 2.11)
Depends: libtinfo5 (>= 5.6+20070908)
Depends: readline-common
libtinfo5
Depends: libc6 (>= 2.4)
readline-common
Depends: dpkg (>= 1.15.4)
Depends: install-info
install-info
Depends: libc6 (>= 2.4)
libsqlite3-0
Depends: libc6 (>= 2.4)
PreDepends: multiarch-support
After that if you want to see if the package is installed in your system simply use this command
dpkg-query -l <package_name>
It will show you if the package is installed, ie
dpkg -l firefox
+++-==============-==============-============================================
ii firefox 8.0+build1-0ub Safe and easy web browser from Mozilla
The ii in front of the package means that its installed.