How to get out of an apartment lease if the landlord broke the contract?

Your grounds for terminating the contract would be, as you note, the dorm's material breach of contract, by allowing smoking in a dorm you signed up for because it was non-smoking; and possibly also breach of your right to "quiet enjoyment" and of the "implied warranty of habitability" due to the marijuana smoke, which prevents you from having undistrubed enjoyment (use) of the premises and also raises health issues.

Note that for all the above, the dorms must have been on notice of the marijuana smoke and also that it was affecting you--i.e., you must have complained to them about the situation, and also have given them a chance to have done something about.

Assuming the above is true, then procedurally, you have two ways to go, if you insist on getting out of the dorm and cannot work things out voluntarily with the dorm:

1) You can provide written notice that you are terminating your lease and giving up possession for the aforesaid reasons, leave, return the key, and then wait to see if they try to sue you for the remaining 3 months under the contract; if you do, you would raise as  defense that they breached the contract and violated the covenant of quiet enjoyment and implied warranty of habitability.

2) You could bring a legal action on a "emergent"--or urgent--basis, seeking a declaratory judgment (or court  determination) that the dorms breached the lease and you may therefore terminate it without penalty; as long as you're suing, you might also seek monetary compensation--e.g. some amount of money back for the time you were subjected to the marijuana smoke.

The first option gets you out immediately and doesn't cost you anything IF the dorm does not pursue the remaining three months, but is riskier--if they sue you and win (i.e. if a court decides that the dorm's actions were not bad enough to warrant terminating your lease), you'll have to pay the money and have a judgment against you on your credit record.

The second option is safer--you don't break the lease unless/until a court says it's ok--but even on an emergent basis, will take a few weeks and will require you to initiate a lawsuit.

Other options:

1) Call the police on the drug users--if they are arrested, that may solve your problem.

2) Don't break the lease (it's only 3 more months, from what you write), but sue the dorms for any health damage and/or medical costs.