Understand the material:
The most fundamental aspect of conserving anything is to understand what you're dealing with. No two materials are the same and as a result, they have different requirements and optimum conditions if you want to ensure their survival. Whilst some need warm and dry air, for others this will cause them to crack and break.
Heat & dryness:
Heat and more particularly central heating is perhaps the single greatest threat around anyone's home to their antiques and collectables. With the exception of metals, most materials are negatively affected by it. This is especially true for "organic" materials such as wood, ivory and lacquer which will dry out and crack if exposed to too much heat for too long a period.Whilst the effects might not be visible at first, over time you will inevitable notice damage which is oftentimes irreversible.
Prevention: Never store antiques near a radiator or a fireplace. If you have smaller wood, lacquer or ivory items, it's sensible to put them into a display case of some kind with a small cup or source of water. This will evaporate and create humidity ensuring that your items don't dry out. On a side note, some art dealers, especially specializing in Asian antiques will actually use humidifyiers (typically employed in terrariums) to replicate this effect.
Moisture & damp:
Thankfully today these aren't quite the same threat as they once were in most people's homes. However they are something to be cautious about especially when envisionning storage in a garage or attic. Damp is especially dangerous for paper and fabrics and even a small amount can completely destroy a work in a couple of minutes. Prolonged exposure can lead to fungus, warping (in wood), discoloration, rust, oxydisation and staining.
Prevention: There is little that can be done other than to ensure that your antiques don't come into contact with it in the first place. Proper storage is key. For smaller objects, keep them in sealed (ideally plastic) containers out of the way of any wet. If you have damp on the walls, don't hang paintings or rest furniture against them as the moisture will seep on through.
One of the most commonly overlooked dangers facing antiques. Sunlight bleaches and causes things to fade. In some cases, this can occur far more quickly than you would think possible especially with things such as watercolours. Once more, damage can be irrevesible. Even furniture will, over years, become bleached. Sunlight can also increase heat. Bear in mind that glass will magnify its itensity and effects.
Prevention: The simplest course is to keep your antiques out of the direct sunlight both through their positionning in a room and potentially also by covering them up with a thick cloth. Remember that the sun swings round throughout the day. What might be safe in the morning, might be in full blaze of the midafternoon sun come 3 o'clock.
Insects, pests and parasites:
These come in various forms and can vary depend on the country/region that you live in. Whilst some such as woodworm will directly attack and damage your items, others will do so as more of a by product "by accident". This isn't necessarily much of a consoloation if you've found a prized possession to be damaged beyond repair. Items most at risk from pests are made out of organic materials such as wood, paper and fabric. Mice and other rodents can also pose a threat as they will eat paper and chew through upholstery and make their nests inside of furniture.
Prevention: It's important to both treat and prevent parasite infestation. For the most part, this is done by use of chemicals and poisons commonly available in most shops. Some of these can be quite nasty, so take great care when using and be sure to read the guidelines accordingly. Preventing parasites means basic maintanence, taking precautions with new acquisitions (never put a parasite infested item next to "clean" ones) and keeping a wary eye open for potential warning signs such as holes, nibbles, excrement, etc.
Pets & children:
Unfortunately, many an antique has been unwittingly destroyed through a moment's carelessness and an overeager child or pet. Dangers can range from precious statues being turned into toys, to unintentional bumps and drops, to dogs and cats chewing and clawing at furniture.
Prevention: Not much can be done other than keeping antiques out of reach, perhaps in the case of young children keeping your treasures locked up behind glass. For pets & furniture, whilst there are some spray products available out there which should notionally keep them at bay, this author has personnally never had much luck with them. It's best to keep an eye on them and discipline them young to ensure that they don't think that it's acceptable to chew furniture. You can also buy foam and other protective coverings to help shield the legs of your furniture.
Restoration & cleaning:
Shockingly, attempts to repair and restore antiques can sometimes be more destructive than just leaving the item be. This can be both through inexperienced and amateur restorers and poor practice. The big danger with restoration is that it can remove patina and value with it. Some items such as coins should absolutely never be cleaned. Doing so will destroy their value and to some, make them appear as fakes. Others, need expert and specialist skills before any attempt at restoration can be made. Another thing to note is that some cleaning products will actually eat away or otherwise harm your items.
Prevention: Do your research. Don't hand over precious and valuable antiques to unvetted individuals in the hopes that they'll do a good job. Restoration is a lengthy and expensive process. Even for quite "minor" work, you can expect to pay at least a few hundred euros/pounds/dollars for an expert and for it to take some months. Be cautious of anyone who offers very enticing rates and extremely rapid turnover. Ensure that they are a reputable specialist with good reviews and recommendations from other clients. If cleaning antiques yourself, ensure that they are of a sort which won't suffer a loss of value from doing so.
These are just a few tips that should hopefully ensure that your precious antiques and possessions are cared for and spared some of the key elements which might otherwise lead to their steady decomposition.