My pocket guide was referring only to Tate Gallery and brougt me to Millbanks.
I was kid in the fog until I turned back to internet and discovered there are 4 Tate Galleries. So this post is solely for those who search the way to Tate Modern.
Visiting Tate Britain is was also great - there will be separate post about it.
If you want to plan your journey ahead use this helpful site.
Address: Tate Modern, Bankside, London SE1 9TG
Website: Tate Modern
Tube stations: London Bridge, Southwark.