Praise be to Allah, and peace and blessings be upon the Messenger of Allah. To proceed:
Taking the proper means does not contradict reliance upon Allah (tawakkul). Rather, it is part of what Islam prescribes, while believing that benefit and harm are in the hands of Allah, and that He, Glorified be He, is the Creator of both causes and effects.
For a means to be valid, it must:
Have a genuine connection to the intended result, and this is known through Islamic teachings, experience, or common practice.
Be lawful and permissible. A lawful objective must not be sought through a prohibited means.
Be accompanied by the absence of attachment of the heart to the means itself; rather, reliance must be upon Allah alone.
As for the extent to which one should take the means, there is no single limit that applies to every matter. Rather, it varies according to the matter and its circumstances. Taking precautions against a serious illness is different from taking precautions against a minor illness; protecting valuable property is different from protecting something of little value; and the means of seeking provision differ from the means of treatment or raising children.
The standard for determining whether someone is being negligent or excessively cautious also varies according to circumstances. It is generally recognized through custom, experience, and the circumstances of people.
Therefore, true reliance upon Allah is: taking the lawful means without neglect or excess, while the heart relies upon Allah rather than upon the means themselves.
And Allah knows best.