There are three basic strategies. Secure from below, secure from above and "magic dust".
Here is a previous post on this
I have no access from the bottom, would prefer not putting holes in the top. What is magic dust, how does it work and where can I get it?
Corn starch works well. Simply spread on floor and work in between the cracks. Remove what is left. The whole idea is to provide a lubricant between the boards where they rub against each other. Some people even use WD-40 they spray it between the joints and wipe the over spray away. It will not harm the wood but will quiet it down.
If the squeak is coming from a loose nail or loose sub-floor board below the only fix is to open from below and fix or using a tiny finish screw method.
How do I stop my wood floor fro separating?
Ray the magic dust is corn starch as woodbridge mentioned above. The squeaks are from wood to wood movement or wood and nail movement. In the latter case some of these are not actually the flooring itself but often the plywood subfloor squeaking on the floor joists. In those case screws are the answer.
When I am doing a hardwood install one of the many prep steps is to thoroughly go over the entire room and secure any issues with the sub-floor. In the case of my own home I used a full 5 pound box of cabinet screws to "beef up" the sub floor to joist connection in my 350 sq foot living room. In the newer part of home (master bedroom addition) the sub floor was glued and screwed to I-joists. New I joists are flatter and do not tend to move like dimensioned lumber.
@ Lynn T....most floor separations have to do with humidity swings. Some woods are less prone to expansion. One criteria when installing any solid flooring to ensure that is is fully acclimated to the homes temp and humidity levels...this often take weeks. Wood is a hygroscopic material in that it absorbs and releases moisture in relationship to its environment, the more stable that environment is the better behaved your floor will be.
Lynn, AS KMS said, floor openings between boards is caused by lack of humidity in the home. This is a very common condition when a new floor is installed before the wood has acclimated to the humidity level within the home. We see this a lot in older homes as we improve them we begin to lower humidity levels that in the past were normally higher. Raising the humidity level in the home will stop the shrinkage, but it also has some detrimental effects elsewhere. Higher humidity levels can warp fine furniture, It can cause mold within wall cavities, it also raises your cooling costs as AC systems fight to lower the humidity that has been added. The result there is the AC will run longer costing you more overall to cool the house.
Lynn I have an example of this in my own home...just in front of our woodstove in the living room ( beyond the granite hearth) the hard wood has 1/16 to 1/8" gaps. The floor here often hits 100 degrees or more when the wood stove is cranked up. Our wiener dog loves to hang out here in the sauna like conditions...but with the increase in temp...the relative humidity goes way down. The flooring in other parts of the room is just fine.
I have owned several homes that had squeaky wood floors and I always used baby powder. It has never failed. However, the home I grew up in had squeaky floors that always let my parents know what time I came home(lol). Something to think about.