Descriptive quantitative methods, also called observational methods, involve observing subjects with no intervention. A case typically studies information from just one subject. A researcher may conduct a case-series, several related cases, to strengthen her research. Cross-sectional studies have a researcher study a sample of subjects and determine variables of interest and their relationship to one another.
Longitudinal or prospective studies are a type of descriptive method and involve setting one or more variables before the study, then determine outcomes after a certain amount of time. Case-control studies allow a researcher to compare a sample of subjects with certain attributes to a control group of subjects who don't have that attribute.
Experimental approaches to quantitative research require some kind of intervention on the researcher's part beyond basic observation. Time series experiments involve a researcher taking one or more measurements on subjects before and after a treatment or event. Single-subject design involves taking repeated measurements before and after the intervention on one or more subjects. Time series might give faulty data because your data may change for reasons other than the intervention and variables you've determined.
Each method offers a different quality of evidence. Case studies offer the weakest quality of evidence because they focus on only one instance or subject, but a series strengthens evidence. A cross-sectional or case-controlled study may provide quality evidence for the absence of a relationship, but it may only suggest a casual positive connection between two things. Consider the nature and goals of your quantitative study carefully before choosing a method.