I will be happy to answer your question but you have to give more details as to what contingencies you are referring to.
If I were you, I would hire a realtor to help you in the process. You can post your town and state so that professionals in your area can correspond with you.
The key word in your question was 'plan' -- it takes planning and strategizing to make this work, but it can as long as everyone involves understands the process, and respects each other!
It depends on which type of contingency you are referring to, but most sales contracts have some type of contingency be it for an appraisal or home home inspection. There also could be the buyer or seller needs to find a new home before the one in question can go to settlement.
For our contingency buyers (assuming home sale contingency), the first thing we do is a preliminary valuation on their home to know what funds will be available to work with for the purchase. We then get you pre-qualified with a good LOCAL lender and do some preliminary home searches and viewings to make sure their is something out there in your price range that will tempt you away from your existing home. Then we get your existing home on the market for sale. Once it appears that the showing levels and interest indicate an offer will be coming soon we start looking for homes again. We would want you to pick at least three (or more) homes of interest since sellers are usually apprehensive about home sale contingencies we want one that will definitely work with you. Once your new home is secured we work with the dates using a pre-occupancy or post occupancy settlement agreement to make sure that your transition from one home to the next is relatively seamless. Best of luck and make sure you choose an experienced agent to assist you!