A snagging inspector will take approximately 3-4 hours to methodically walk through each room and outside the average property depending on the construction and finish. Photos and notes will be taken of all observed defects, poor workmanship and any serious problems that would not comply with building regulations which will later be entered into a report and sent to the home buyer. The home buyer will forward the report onto the property developer who is responsible for ensuring the defects/snags are rectified.
Once the overall construction and finishing is complete a snagging inspection can be undertaken. The ideal time to have a snagging inspection would be before completion however after completion is acceptable. If undertaken prior to completion it allows the developer plenty of time to rectify the snags before the property is moved into. The other advantage is that the developer cannot dispute that any of the snags were caused by the owner after the property was moved into. A snagging inspection can be carried out up to two years after completion even though the ideal timeframe is prior to completion. Developers usually prefer for the inspection to be undertaken early on so it is easier for them to get the various trades back in to rectify any issues while the site construction is still present otherwise the the developer has to pay additional costs to send in contractors later on. 

Major defects that do not comply with NHBC standards should be rectified urgently and prior to the homebuyer moving in to prevent any danger to inhabitants. Other defects will depend on a number of factors such as location within/outside of the property, ease of repair/replacement and the nature of the defect. If a replacement is required for a door or window for example this may require a few weeks wait. Minor cosmetic defects such as poor caulking or paint finishes can be repaired within a few days. Timeframes will depend on the developer and how fast they are to address and fix and of course how helpful they are willing to be.  
Specialist knowledge is required to undertake a snagging inspection which is why it is beneficial to use a professional. Industry experience and knowledge of various trades ensures a professional will know what to look out for and spot issues the untrained eye will not see. 
A property developer should pay for the cost of fixing all the snags in a new buid property
The average new build buyer is unlikely to know what to look for when reviewing the property which is why using a professional snagging company useful. A UK new build property has 100 snags on average. Ensuring any defects/problems are addressed early on prevents personal costs, time and effort for the home buyer. 

The property is still owned by the developer until completion. If the developer will not agree to access your solicitor will be able to arrange as you have a legal interest in the property.