Hi Josie,
To save seeds for long term storage, it all depends on what you plan to do. If you want to save seeds indefinitely, in a a freezer in airtight containers is your best bet. You must make sure the seeds are dry though or you will kill them. You must always let the containers come to room temp before opening or you will kill the seeds. If you plan on a lot of seed retrieval for trading this is not the best method.
You can store in the fridge in airtight containers. Make sure they are airtight since moisture is not good. There is an exception to this some seeds like spring woodland ephemerals and a few other types of seeds need be keep cool and moist in storage or they will die. Most seeds though need to be dry. In the fridge is good if you have a warm humid home.
If you have an area of you home that stays relatively cool and dry and does not fluctuate in temperature much, most seeds will happily stay there for quite some time. The sum of the temp and humidity should not exceed 100 when added together. Like 70 degrees and 40% humidity(high end of normal for a home in spring/summer) equals 100. During winter it is not much of a problem since humidity in homes is low. In summer though if your home is not air conditioned and it gets to be 75-80 degrees inside and very humid like 60% in summer, you are putting seeds into conditions they don't like because the total has risen over 100.
I hope this helps,
Remy