Dlight to Slight
A very simple combo that is true at low to mid percents. Also good damage and chase dodge followup potential.
Dlight to GC Nlight
Another great combo that is fairly simple that can be performed at any percent, with nlight's potential to kill at high percent it can make for a kill confirm.
Nlight to CD Slight
The only followup off of Nlight and the timing can be a bit strict for it be a true combo. This can only be done at low percents due to the amount of force that Nlight has.
GC Dlight to CD Rec
This is one of the harder combos on Hammer but is really rewarding due to the placement of the opponent and the stage bounce or throwing them off stage for edgeguards. Can be done at any % with proper postitioning.
Dlight to Sair
This is your main kill confirm with Hammer, can only be done at mid to high percents, timing can be a bit strict for a true combo but very useful nonetheless.
Russian Mafia (Dlight CD Recovery Dair)
Russian Mafia named by Berthen/OmniPie is an infamous kill confirm hammer combo that is very technical and difficult but the reward is great. This can only be done at high %'s.
Dlight to Dair
This combo is very useful, can be used for kill confirms or if you wish, you can do this to follow up with Sair or Nair depending on where they end up.
Generally when you play hammer, your goal is keep your opponent at a distance until you want them to be in your personal space. So that would consist of doing nairs when they are slightly above you, and throwing out a lot of sairs, if you time it right you can hit your opponent on the ground and potentially go into something like dlight to get something like sair, gc nlight or slight. Be careful doing weapon throws because it doesn't hit point blank like most weapons, which makes hard to properly follow up on.
Hammer's Edge Guarding is fairly strong with Ground Pound doing a lot of damage and has a lot of priority and force. Certain characters have signatures that has a small hitbox that will hit opponents that are hugging the stage wall. Down light can also perform this. Hammer's recovery can also kill characters off stage but is a bit risky since you would have to go under the opponent to land recovery which can be punished if they see it coming.