First check your facility guidelines.
If you are saline locked...I flush...then will push medication...followed by flush and lock. Time slow and steady over whatever the recommended time period is.
If running iv that is compatible....clean port closest to patient....and again, push med for recommended time period.
As far as, narcotics...depends on where you work and who your patient is. Opiate naive, I always will dilute and do slow push(even with fluids running)....sickler...no dilution and pushed over one minute(with fluids running). Also need vitals prior and q 15 with pain reeval.
Other meds require monitoring, cardizem, labetelol, other cardiac etc. also require different amounts of time for push. Always check...if something like an AFib....you may need to monitor then note when and if a rhythm change occurred.
Meds like Lasix must be pushed slowly or deafness can occur...I am sure there are a million more suggestions.
My suggestion, follow your med book and monitor your patients for their reactions. Hope this helps.