First, are presidents able to invoke the act whenever they feel its necessary? What’s the process for the act to be invoked?
Here is the text of the code. The part shall take such measures as he considers necessary, appears to answer the first question. A proclamation to disperse and a signed order to the Department of Defense to activate troops would invoke it.
10 U.S. Code § 253 - Interference with State and Federal law
The President, by using the militia or the armed forces, or both, or by any other means, shall take such measures as he considers necessary to suppress, in a State, any insurrection, domestic violence, unlawful combination, or conspiracy, if it—
(1) so hinders the execution of the laws of that State, and of the United States within the State, that any part or class of its people is deprived of a right, privilege, immunity, or protection named in the Constitution and secured by law, and the constituted authorities of that State are unable, fail, or refuse to protect that right, privilege, or immunity, or to give that protection; or
(2) opposes or obstructs the execution of the laws of the United States or impedes the course of justice under those laws.
In any situation covered by clause (1), the State shall be considered to have denied the equal protection of the laws secured by the Constitution.
10 U.S. Code § 254 - Proclamation to disperse
Whenever the President considers it necessary to use the militia or the armed forces under this chapter, he shall, by proclamation, immediately order the insurgents to disperse and retire peaceably to their abodes within a limited time.
Also, it wasn’t clear to me why the act is necessary. If the national guard is active what additional use does the Insurrection Act have?
All current National Guard activations were by the governors. Activation by the president would "federalize" the guard and, therefore, transfer control, possibly, to the United States Northern Command (USNORTHCOM). It would also allow active duty units of the military to be sent in to support the operation.
The Wikipedia entry for USNORTHCOM mentions domestic operations and training and the Insurrection Act.