If you think of the offset as a small voltage source in series with one of the inputs, just before the input, you can compensate by introducing the opposite voltage at the inputs, in whatever way you like.
One method, if it's an inverting amp, is to replace the ground connection at the + input with a small adjustable voltage. This is probably easier to adjust if you put the trimmer between two larger resistors that soak up most of the supply voltage, leaving only a little dropped across the pot.
For a single supply circuit, it changes a bit because of the issues with combining dividers and the way all the currents through the resistors interact; you don't want two dividers talking directly to each other. If you've already got a divider at + you may be able to just put a trimmer in the middle. Simple.
It's also possible to sum a small offset into the inverting input. Check "summing amplifiers" if you aren't already familiar. Here you also have to think about combined impedances and how the current will flow; a simple voltage divider feeding a summing resistor becomes part of the feedback network of the amplifier, so the voltages will get wonky. This is a good place to use a buffer: from the adjustable voltage divider, to the buffer amp with low impedance output so it can't get pushed around, through the summing (scaling) resistor, to the summing node of the amp. This isolates the adjustment divider from the feedback network and gives you simple control of the voltage. And here, you can use a big summing resistor to scale the divider voltage way down, so it's easier to adjust. And of course the three-part divider trick.
It isn't always necessary to fix it at the first amp's input(s); you can fix it at the next stage or somewhere else in your circuit.
And depending on what you're doing, if your signal is AC, you might be able to just use AC coupling to block the offset.