This is a bit of a broad question. Equipment-wise you will need the same as any other beer. Lagers differ from ales mostly in terms of fermentation, as they are bottom-cropping, typically ferment at lower temperatures, and are lagered (store for an amount of time at low temperatures).
So you need:
- A malt mill or order your malts crushed
- A way to mash your malts (mash tun, brew-in-a-bag + kettle, electric kettle etc.). If you want to go more traditional it would be nice to be able to step-mash or do decoction mashes
- A way to boil your wort (Pilsner malt is quite notorious for having high amounts of DMS so you want a good vigorous boil)
Pretty much the same as any other beer to be honest
Then there are the nice to haves specifically for lagers:
- Ability to temperature control your fermentation. Traditionally lagers are fermented at low temperatures (10 to 12C) so you would want to be able to cool down the fermentation and keep it there. You can cheat your way a bit by fermenting at a bit higher temperatures (brulosophy.com has some interesting findings on this) or using a strain like California Lager, which imparts lager characteristics when fermented at higher temperatures.
- Ability to lager your beer - this can be as simple as storing your bottled beer for 2+ weeks in a fridge at 0 to 6 degrees C so no extra equipment needed.
- Water treatment (depending on style) can make a big difference to a lager. Not a must-have, but definitely a big factor in making the perfect lager.
- You will most likely want a clear lager. A lot of factors play into this: a protein rest during the mash, adjusting the pH of the mash, oxygenating the wort before fermentation, selection of lager strain (some flocculate more than others), fining agents used in the boil or after (protofloc, gelatin etc.), but most importantly the time and temperature you lager at. Longer is often better. Again not a must-have but definitely nice to have.