Dairy is relatively easy to substitute, thanks to the ever-growing array of non-dairy products available. You don't even need to visit your specialty health food store, as many are available at your regular supermarket.
Replace same quantities in a recipe with any of the following milks:
Personally I like to stick to rice milk as it is much more palateable, although when baking, there is no discernible difference.
You can also replace liquid quantities with either fruit juice or water, but overall result might be a little on the bland side.
Most commercial margarines contain milk solids, so Nuttelex is by far the best non-dairy margarine available. It is also soy-free and the only non-dairy margarine I have come across with no preservatives. Tablelands make a dairy-free spread, and there is also an unsalted kosher margarine called Migdal made in the US and available here in some shops. Loaded with preservatives though, hence I steer clear. Would be lovely if Nuttelex made a salt-free version which would work perfectly in your 'buttercream' frostings.
Soy is pretty much the only non-dairy cheese substitute available. Please remember to check labels as some soy cheeses actually have casein in them (dairy protein). Kingland International make a block of soy cheese, Redwood's Cheezly is sometimes available at healthfood stores, but Tofutti is really the only brand readily available in Coles/Woolworths. They come in very convenient plastic-wrapped individual slices (both American-style cheddar and mozzarella for melting). Beware though that Tofutti generally (being American) is uber-processed so occasional use is ok - but I wouldn't go serving it on every sandwich if you can help it.
You can use Parmazano as a parmesan replacement to sprinkle on pasta - it is made predominantly from seasoned soy powder - you could feasibly make your own if you visited your local health food store and sourced the individual ingredients.
Soy - both Kingland and Tofutti produce this - good for any replacements, the consistency is identical to dairy cream cheese. (I have served smoked salmon, dill and cream cheese sandwiches before and no-one could tell the difference). Also good for cream cheese icing on carrot cakes but make sure you use a recipe that includes some shortening like butter or margarine (use Nuttelex obviously). Combining it with icing sugar seems to highlight the high water content and goes very sloppy.
Tofutti again - also a good substitute for yoghurt in cooking (rather than yoghurt for eating).
Kingland make a good fruit soy yoghurt in packs of four and individual larger tubs also. Available from Coles - there are some other soy yoghurts on the market but check ingredients always - some have traces of dairy or nuts.
Coconut cream can be used if your sweet recipe lends itself to a coconut taste.
Soyatoo make two versions of soy cream - one for whipping and one for cooking. If you don't mind the soy taste, it can make an ok substitute. I have seen some rice-based creams in shops like Sunnybrook but they stock it sporadically. It's called BioAvena, comes in UHT pack and is purely vegetable based (soy-free too). Works well in creamy pasta sauces.
Until it's readily available though, we tend to adjust our menu so it's not necessary.
I have attempted this once, when I was desperate to make a lemon slice. It took the better part of a morning to bubble away on the stove and reduce to the proper consistency, so be prepared to hang around. If you make a big batch, it might well be freezable - though I haven't tried it.
3 cups soy or rice milk
½ cup white sugar
1 tbsp vanilla extract
pinch of salt
Add the soy or rice milk and the sugar to a saucepan. Cook over medium-low heat, stirring constantly, until volume is reduced to 1 cup. Add a few drops of vanilla to taste, and a pinch of salt. Cool before using. May be stored in the refrigerator.