I'll take into consideration of the fact that unless I did a really good job of hiding my traitorous intentions then the Monarch I plan to overthrow is more than likely either a complete moron or disturbingly gullible. So I won't bother to explain myself if/when the Hero exposes my evil plans to said Monarch.
Rather than killing off the king's children to secure my own hold on the throne, I will slip the king or queen hormonal tablets to sterilise them and induce embarrassing illnesses (which may aid in my attempts to seize power). If they already have children, then I will endear myself to them from a young age to secure the same position when they take over, and then employ the same tactic.
I will be aware that the above plan will take up a lot of my time during which I will not get any younger and might become impatient enough to make a mistake. Therefore I will also pay attention to the following tactics:
Make sure that I am the Guardian of the royal children should any unfortunate accident make them next in line for the throne, and that I am the one to take over matters of state until they are of age.
Resort to tactics that will apppear unwise at worst, rather than expose me as an enemy of the current rulers if a pesky do-gooder reveals them. For example, rather than secret murder attempts on the Royal Brats, I will spoil them with toys and sweets to the point where they become living proof that Aristocrats Are Evil and the people are grateful if a concerned politician steps in and seizes the political power.
If possible I will ensure the royal doctor is in on this scheme to explain away any side effects as a natural illness.
Said doctor will be my patsy if it comes down to it.
If possible I will try to be a Villain with Good Publicity in the eyes of my Liege's subjects, allowing me to slander the effeminate king/overly masculine queen and come out on top in the inevitable coup.
Should a suitor turn up for the (single) current monarch or one of their heirs, whom I am currently trying to court, I will immediately do a background check and expose him as a commoner.
If the queen/princess/"progressive" king happens to like them for this reason (or they turn out to really be a prince) I will take full credit for avoiding what could have lead to misunderstandings. Then, when their relationship is in its early stages, I will plant evidence of an affair and catch the monarch on the rebound after the breakup.
Should a suitor turn up for the married monarch I will play this to my full advantage. Why bother to fake evidence of an affair when there's potential for a real one, after all?
No, I should already be familiar with all of the Lists before putting any plans into action.
I will also assume that the monarch, any heir(s), and anyone else who can ruin my plans is doing the same. Also, I will endeavor to find the Spanner in the Works and remove him from the equation as soon as it becomes feasible.
I should note that taking over the kingdom is optional. The cost/benefit ratio sometimes favors remaining the chancellor, especially if the existing ruler is enough of an Unwitting Pawn for me to control completely.
This especially includes cultures which sacrifice kings.
If the monarch is too Genre Savvy for me to control, I will simply enjoy the benefits of being able to speak in the name of someone with absolute power. It's almost as effective as ruling myself, but with much less hassle.
If I meet the hero face-to-face or find out that he knows any part of my plan, I will set things up so that they can be reasonably pinned on my Bastard Understudy. No, screw it, I'll set things up like that the whole time, preferably by convincing the fellow that he can act as the Man Behind the Man when I take over and having him do all the work.