Hi Jammie - longtime meditation person (and depression/anxiety sufferer and someone who used to drink way way too much !). My first advice would be to make sure you have done everything you can in terms of emotional and medical support (I guess you have seen GP about mental health, thought about alcohol councelling, maybe AA etc etc. ?).
Meditation is best learnt from a teacher (I speak from experience!) Many Buddhist centres have classes / courses (which is how I learnt), some yoga teachers teach it too, but it is often not the main part of their practice. 'Mindfulness' practice (also taught at many Buddhist centres and also by many psychologists and Cognitive Behavioural Therapists) is also very useful - it's something I use (as often as I remember to!).
If you can't find a teacher / centre, then CDs / DVDs are probably your next option, but I cannot stress the importance of a good teacher enough, especially during the early stages of learning. Most (but not all) Buddhist centres teach meditation and you do not have to 'convert' or be a committed Buddhist to meditate (in any case, the core of Buddhism is to meditate and be mindful and let go of negativity.) There are also a few 'secular' meditation groups around.
If you want to find somewhere to try out, I'm sure a quick Google search will tell you what is in your area.
Hope that helps. If you get stuck, please shout!