The national average time it takes to close a house is 50 days. This gives everyone time to do their due diligence. The deadlines are spelled out in the contract. The biggest responsibility of the Buyer is to get all their paperwork to the mortgage company. A closing could done in 30 days if the Buyer was proactive and got a preapproval from the lender. With a hot market this is usually requested by the Seller so they are able to assess the Buyers ability to purchase the house. While this is being done the Realtor and Buyer should schedule an inspection. It is good for the Buyer to meet the inspector at the end to go over any defects or helpful maintenance tips for the house. Once the Buyer and Seller agree on any items that are either deferred maintenance or health and safety issues to be fixed the lender will order the appraisal. You should allow some time for this as they can get busy. There could be some other approvals on the lending end depending on the type loan like FHA or Rural Development. Once the lender has all the approvals,paperwork and appraisal they submit the file to underwriting. They may want additional paperwork so this takes a few days. Purchasing a home with cash can take as little time as 10 days to 2 weeks. The appraisal is optional so you only need time for title work to be done.
Things that can delay a closing could be contingencies like the Buyer needing to sell their home.
The Buyer should not do anything in that time period that might change their credit score or debt to income ratio. Getting insurance should be done asap as with older homes insurance companies might require additional items to be addressed. Appraisers might also have a to do list especially if it is an FHA loan. If the appraisal comes in lower than the contract price the parties will need to renegotiate. It is a stressful period so the best thing is for all parties to communicate as much as possible..