This is a topic that comes up quite a bit on MFA, so I've complied advice from various posts into the definitive guide. I hope it helps!

The basics
Batch similar colours to cut down on loads. T-shirts and shirts can be washed together. Have a mix of underwear colours so no matter what you're washing you always have underwear.
A front-loader washing machine is far gentler on your clothes than a top-loader. Hand washing is best, but hey, who has time. (Bonus: front-loaders are usually more efficient in water/power usage and better for the environment)
Use less detergent than recommended - past a point more detergent doesn't mean cleaner, it just builds up in your clothes.
Just because it doesn't smell, doesn't mean it isn't dirty
The only items that should ever go in the dryer are underwear, socks, and possibly undershirts. Everything else should be hung to dry. Get a cheap fold-out clothes rack to dry your clothes on.
Tumble dryers are brutal on clothes - even on delicate settings they are too hot for most items, and the tumbling will wear out the clothes very quickly. All that lint collected in the filters? That's the fabrics wearing down.
Never dry clothes in the sun (except for whites) - it will bleach the colours very quickly.
Dry cleaning is very harsh on your clothes, try to keep it to the minimum

Socks and underwear
Socks and underwear should be washed after every wear, no exceptions.
Washed on warm cycles (30 C, 80ish F)
Can be dried using a dryer - these are the only items you should ever consider using a dryer - everything else should be hung to dry.

T-shirts, undershirts, sweat shirts and polo shirts
T-shirts, undershirts and polo shirts - basically anything very close to you skin - should be washed after every wear, again, no exception.
Sweatshirts can be washed infrequently, assuming you're wearing them over a t-shirt, after every 5 or more wears. This is solely dependent on how they're treated and how dirty you think they're getting.
They will usually be ok with warm water (polo shirts may need a cold cycle)
Gently pull them into shape before hang drying or flat drying for sweatshirts.

Dress/business/button-down shirts
Should be washed after every wear. If you wear undershirts they can be worn 2 to 4 times before washing, depending on what sort of treatment they get while being worn, what sort of environment you wear them in.
A good quality shirt, treated well, should last hundreds of wears and washes.
Washed on the most gentle cycle in cold water. Hand washing is better, but time consuming. Some guides say that shirts should be put in a delicates bag to protect the collar points and cuffs, I've never found that necessary.
Shirts should only ever be dried on a wood hanger to keep the shape - Ikea hangers are great for this. Never user a wire hanger - you will ruin the shape of your shirts.
Under no circumstances have them dry cleaned, but laundered is OK, although they will not last as long if you send them out for laundering.
If your business shirts start to get stained around the collar, a bi-carb of soda paste massaged into the collar and left for 10 mins works, other methods use a vinegar and liquid detergent mixture.
If your underarms get a build-up that smells when you wear them, dipping the underarms in a 50/50 cloudy ammonia/water mixture and letting it sit for 10 mins is good for this. This also works well for t-shirts.
NEVER re-iron dress/business shirts after wearing them once - you're cooking the sweat, dirt, dust etc. into the fabric and significantly increasing the likelihood it will smell after a short time. Ironing a shirt is not the same as washing it - it doesn't clean it.

Jumpers/sweaters/cardigans/knits
Anything wool should generally be dry-cleaned, unless it explicitly says machine wash
Then, only on cold, gentle settings, with a slow spin. Or even better hand wash (but never wring them out)
Use a gentle detergent designed for wool.
Knits should be gently pulled into shape, if required, then dried flat (that is, horizontally), either on a fold out drying rack even better on a pop-up mesh rack. These can be bought very cheaply.
Never ever ever put these in a dryer.

Anything silk
Extra gentle hand wash in cold water, with a very mild detergent.
Hang dry only
Dry cleaning is generally out of the question, unless you go to a specialist cleaner

Jeans/chinos
Jeans/cotton chinos should be washed every 4 to 8 or so wears (you be the judge) or if the knees are starting to stretch out. Cold wash only.
Exception - raw denim should not be washed, but soaked every 6 months to a year or even longer.
Hang dry only.

Linen suits/trousers
Linen trousers can be hand washed, cold only with a gentle detergent, or dry cleaned very occasionally. Hang dry only.
Spot treatments on light coloured linen will show, so use with caution
Linen suits should be dry cleaned only very infrequently (eg once a year). Even thought you might be washing the trousers, have the trousers and coat dry cleaned together, so if there is any fade from the dry cleaning you don't end up with a mis-matched suit.
Especially with light weight linens, dry cleaning will wear them out very quickly.

Suits
Suits should be dry cleaned only and very occasionally - usually once a year is enough, possibly more for lighter coloured suits.
Steamed gently in between for shape/wrinkles and the pants pressed for creases. Hanging in a steamy bathroom is a good method if you don't have a steamer.
You shouldn't wear a suit two days in a row - after you wear it it should be hung on a good quality hanger (to keep the shape), gently brushed and aired for a day or two.
If you press the pants yourself, don't iron directly on the fabric, it will go shiny - use a damp ironing cloth
If any suit claims it is machine washable, you should not be wearing it in the first place. Burn it.