Part of the job of the US constitution and legislature would seem to be to offer checks and balances against the actions of the President. Why has no-one yet used any of these powers to try and rein in or remove the President? What steps would there have to be, now, in order to begin such a process?
Expanding on indigochild's answer a bit...
Impeachment proceedings are brought in response to "high crimes and misdemeanors", which aren't explicitly enumerated anywhere, but are generally understood to be gross abuses of power, dereliction of duty, obstruction of justice, or other betrayals of public trust.
You don't get impeached for being bad at your job, or for being nakedly political in appointments or firings. The President has a lot of freedom to staff the Executive as he or she sees fit. It's just that in the past, most American politicians had a concept of "shame", and usually avoided doing things that appeared dishonorable (or at least covered them up more effectively).
The House has to choose to bring articles of impeachment, and they may be perfectly happy with how and why the President fired Comey (because let's face it, Comey did not cover himself or the Bureau with glory over the past year). If the House did bring articles of impeachment against the President, then the Senate would have to choose to convict him and actually remove him from office.
Now, if it's true that the President has admitted that he removed Comey specifically because of an FBI investigation into conflicts of interest or criminal behavior by the President or his staff, then we've clearly crossed the line into "high crimes and misdemeanors" territory (obstruction of justice) - that's part of why President Nixon was impeached.
The US is in an unfortunate situation where politics matter more than literally anything else, so this Congress is unlikely to impeach this President for anything short of outright treason unless it seriously weakens the Republican Party's chances in future elections. Congress may choose to censure the President, which has no real effect other than to be an official "Bad dog! No cookie!" admonition.
40-some-odd years ago, Congressional Republicans convinced President Nixon to resign rather than face impeachment, but not out of political concerns - to them, it was genuinely better for the country that the President not be forcibly removed from office.
Ultimately, the fault lies with us, the voters. We truly get the government we deserve, and right now we deserve the most indolent, venal, petty, and incompetent government imaginable. Political literacy is at a dangerously low level in the US right now, combined with a strong anti-intellectual and narcissistic bent.
Unfortunately, we get to inflict the results on the rest of the world.