It really depends on which natural remedy you are using. St. Johns wort, for instance, can be as effective as certain anti-depressants, according to the Cochrane institute. However it is understudied in the medical community. Other natural remedies such as certain foods and dietary methods have been studied more broadly, and there seems to be a general idea that certain natural foods and drinks can help with brain chemistry, and ultimately lower anxiety after consistent consumption. As far as timing goes, no pharmaceutical or natural relief will have a designated timeline - it depends on a number of factors: compatibility with drug, maintaining a positive attitude towards it, consistent consumption, and environmental factors like external stress. If you, personally, are not happy with the effectiveness of a remedy, it might be time to look for a new one. Give it at least a couple of months though. Also, write up a quiz that gauges your anxiety levels now, then take the exact same one in about a month.
I've heard it can take up to a month to a month and a half for a pharmaceutical anti-depressant or anxiety medication to really start to work its magic; people I know think it starts to work its magic as soon as two weeks. Although with both pharmaceuticals and natural remedies it is not like one day you are feeling like crap, and the next day - boom - it kicks in. It will probably contribute to your overall mood and you will not notice a drastic change, yet one day you'll have an epiphany where you're like "wow, I haven't been feeling as anxious lately". Believing it will work can help too because the body is more likely to just "act better" on its own if it believes something is helping it - i.e. placebo.