Human life support is complicated, bulky, and it smells bad. If we only sent robots we would not have to mess with it. But if we go in person we have to deal with it. First, go to the life support page at Atomic Rockets.
To begin with we will need a cabin. Here there is a big difference between short missions, up to a day or two, and longer ones. Short term passengers can sit in airliner style seats, crew at their work stations, and the galley needn't be much more than a refrigerator and microwave oven. But as missions get longer you need bunk space for off duty crew, and at some point cabins or bunkrooms and a real galley.
From a comparison of railroad sleeping cars versus coaches, sleeping accommodations take up about 10 cubic meters per person, 2-4 times as much room as airliner style seating. Add a galley and dining compartment, storage space, and some this and that brings the minimum requirement to around 15 cubic meters per person, give or take.
(The ISS is much roomier, Wikipedia claiming a 'living volume' of 358 cubic meters for a crew of six, or nearly 60 m3 per person. But I don't know how living volume is defined, for example whether it includes working spaces. Total pressurized volume of the ISS is reported as about 1000 m3.)
Man does not live by bread alone, but along with water and oxygen it is a start. Human beings need about 5 kg/day in food, water, and oxygen, food accounting for about half the total. Unless you have regenerative life support you will need to carry it all with you. This does have the advantage of simplicity - we know how to do it, which is not the case for regenerative life support. For missions up to a few months the mass penalty is not excessive; 200 days' provisions and supplies come to about a ton per person, requiring about 3 cubic meters of storage space.
With storerooms, equipment bays, and assorted plumbing, our hab compartment for deep space transports may thus have a volume around 20 cubic meters per person. This in turn equates to about a ton or two per person for the basic hab pressure vessel, plus another ton or two of fittings and equipment, and for a 6 month mission a ton of consumables. So, altogether, each person (passenger or crew) carried by a transport class ship accounts for 3-5 tons of payload capacity.
In the rocketpunk era the standard way to reduce this was to carry passengers in Cold Sleep. But at our current level of knowledge this is magitech. We haven't a clue how to drastically slow down human metabolism, or even produce mere hibernation, let alone how to do it safely.
Another rocketpunk era classic was regenerative life support, those famous hydroponics tanks somewhere aft/below decks. Details were sometimes vivid, occasionally charming (fresh flowers in the wardroom of PRS Aes Triplex), rarely quantitative.
There is a rule of thumb that it takes 10 kg of food source biomass to support 1 kg of whatever is eating it: thus, for a purely vegetarian diet, about 0.75 tons of plant biomass per person. Biochemistry conveniently sees to it that the plants we eat also replenish our oxygen.
On this basis the break even point for regenerative life support is about 150 days. A 1953 (!) source cited at Atomic Rockets says 145 days. But this ignores the penalty mass of the hydroponics tanks. (Or aeroponics, whateva.) Greenhouse hydroponics on Earth seems to achieve yields of about 30-35 kg per square meter. One source mentions a 4 month growing season, suggesting that with year round operation we might do three times better, approaching 100 kg/m2.
Since we eat about a ton of food per year, this corresponds to about 10 square meters of growing surface per person. With access and working space perhaps 20 cubic meters per person - comparable, that is, to our estimate for living space, and probably with a comparable mass, about 3-5 tons per person, including a ton or so of biomass.
The structure and equipment mass needed to grow food shifts the tradeoff point: For missions less than about 2 years, the mass of stores plus storeroom capacity is less than the mass of a regenerative system. Most transport class ships - which for this purpose includes most military craft - are used for shorter missions that that, so they will dispense with the extra bulk and mass of full regenerative life support. They might have a garden deck, more for human factors than for its modest life support contribution.
There's also the little detail that we don't yet know how to do regenerative life support. This is one type of space research that can be done on Earth, and as space research goes it does not require a lot of expensive hardware. The Biosphere 2 fiasco doesn't prove a lot in and of itself, given the possible flake factor, but building a human supporting ecohab cannot be easy, or someone would have done it by now.
But we won't really need regenerative life support until we are establishing long term stations or bases. And my guess is that we'll learn the techniques gradually, in the process of reducing dependence on costly supplies from Earth. Regenerative life support is, on some level, a sophisticated form of gardening, and gardening has always called for patience.
Two other life support considerations: Radiation, and heat.
Without shielding, the cosmic radiation dose in deep space is about 400-900 millisieverts per year, where 1 Sievert = 100 old fashioned rems. The current career limit is 4 Sieverts for astronauts, 2 Sieverts and change for nuclear industry workers. Thus for long term habitation we will need enough shielding to diminish the penetrating radiation by about tenfold. This requires about 100 grams per square centimeter - a ton per square meter. And this shielding has to be applied all around, because cosmic rays can come at you from any direction.
This is not a problem for big permanent habs, but it is far too massive for transport class ships. This is one more reason to favor fast orbits for human travel. A ship's habitat might provide enough shielding to cut radiation by half, so that a 3 month tranfer mission provides about the same radiation exposure as a year living aboard a shielded hab.
And don't forget plain old heat management. An object at room temperature radiates about 400 Watts per square meter, which you will have to replace - but at 1 AU you are also exposed to a solar flux of 1400 W/m2 on surfaces directly facing the Sun. Managing heat, both from onboard power and solar flux, to keep the hab in the human comfort zone will be a constant task.
In fact, all of life support will be a constant task. In rocketpunk days maintaining the life support system was treated as an afterthought to the cool space stuff like astrogation and engineering. This is unlikely to be the case.
This being All Hallows' Eve, I'll just leave you with this thought for your contemplation: Cascading life support malfunction.
Related post: Spaceship Design 101.