Historically speaking, swords were the most important tool a warrior owned and like any tool, they were (and still are) an investment that needs to be taken care of. While there are thousands of options for the collector, most swords usually require basic maintenance.
If your collection sees any kind of use, always be safe and respectful of the sword itself. Swinging it needlessly against hard and unyielding surfaces can potentially notch the blade, or loosen any fixtures on the sword such as the pommel, hilt, etc. Respect of your tools is one of the core principles of responsible ownership.
Firstly, determine the basics of the sword itself. What kind of steel is it? Is it genuine leather on the hilt? Any sort of precious stones or metals on it? While it seems basic, different materials will require different kinds of care.
Secondly, examine the sword- are there are any areas that need special attention, such as notches, scratches, dullness, etc? Identify those areas first and research the appropriate care methods for the type of metal from leading experts. This can be as simple as a quick Google search, or even recommendations from the crafter who made it.
Sometimes these areas may require a strong buffing using different types of buffing compounds or even sanding with a high-grit paper for a polish. Always be careful when attempting this kind of maintenance, as it is easy to potentially damage your investment through improper care. After that, standard sharpening using your preferred method can be done, followed by polishing and stropping.
Thirdly, once those areas have been identified and tended to, focus on general care of the sword. Most items will come with a coating of oil, or even grease, to protect it during shipping and handling. Generally, this will not damage the item, but care should be taken. If you use a specific type of oil on the blade, strip the existing oil/grease and replace it with your oil of choice.
If the grip or scabbard is made of leather, a light coating of oil can help keep the leather supple and prevent it from drying out and cracking (or even deteriorating completely).
Fourthly, if there is any sort of precious metals, such as silver or gold, commercially available products should be able to maintain most items.
Finally, proper sword storage is key. Typically hanging swords is the best course, as it keeps them from bending over time, but at the very least the items should be kept covered and placed in a safe, clean location.