You can put the start and finish in manually, but that introduces a constraint (task must start/finish on). Obviously you may have a constraint, be it resource, regulatory or otherwise In which case this is fine but if this isn’t the case I think your best solutions has been suggested already without knowing why you want to do it like that.
As has been suggested, the easiest way will be to put your successors and predecessors against each task, set the first start date and then adjust durations until you get the finish date you want.
This is a slightly backwards way of scheduling it but without understanding what your trying to do and I it’s difficult to give any other suggestion. At least doing it that way (provided you have auto scheduled everything) you can easily track the project and any lead and lag will automatically adjust tasks accordingly.