What is better: multiple "if" statements or one "if" with multiple conditions?

The following two methods:

public void oneIf(boolean a, boolean b)
{
    if (a && b)
    {   
    }
}

public void twoIfs(boolean a, boolean b)
{
    if (a)
    {
        if (b)
        {       
        }
    }
}

produce the exact same byte code for the method body so there won't be any performance difference meaning it is purely a stylistic matter which you use (personally I prefer the first style).

Both ways are OK, and the second condition won't be tested if the first one is false.

Use the one that makes the code the more readable and understandable. For just two conditions, the first way is more logical and readable. It might not be the case anymore with 5 or 6 conditions linked with &&, || and !.

One golden rule I follow is to "Avoid Nesting" as much as I can. But if it is at the cost of making my single if condition too complex, I don't mind nesting it out.

Besides you're using the short-circuit && operator. So if the boolean is false, it won't even try matching!

So,

if (boolean_condition && matcher.find(string)) {
    ...
}

is the way to go!

Java uses short-circuiting for those boolean operators, so both variations are functionally identical. Therefore, if the boolean_condition is false, it will not continue on to the matching

Ultimately, it comes down to which you find easier to read and debug, but deep nesting can become unwieldy if you end up with a massive amount of braces at the end

One way you can improve the readability, should the condition become longer is to simply split it onto multiple lines:

if(boolean_condition &&
   matcher.find(string))
{
    ...
}

The only choice at that point is whether to put the && and || at the end of the previous line, or the start of the current.