A full time techie will use the burn-resistant callus on the end of their middle or ring fingers of their non-dominant hand, and if you blink you've missed the whole operation!
For us lesser mortals, it becomes an exercise in juggling board, part, solder and iron without getting burnt. There are two possible approaches - freehand and using some sort of a jig.
For small boards you can do it freehand:
Hold the part in place with a finger of the same hand that's holding the board but, as its a header with solid metal pins that will burn you before you finish soldering them, you need to press on one that you are not going to solder (yet). Bend the end of the solder coming off your bench reel to a convenient angle so you can bring the joint and the iron to the solder. If that's not possible, you'll need to hold the solder (same hand as the board) near the joint to minimise the time you are carrying it on the bit, and use flux on the board. Once one pin is tack-soldered, you can reheat it and adjust how the connector is sitting, then solder the opposite end/corner and then the rest of the pins.
Supporting the board and jigs:
The general approach is to support the board and rig something to push on the part that won't melt. If you've carefully planned the assembly order by height and location, the 'something' can be your bench surface, otherwise you may have to rig something such as a small block of wood on the bench or a piece of card and some tape (or heat resistant tape like Kapton, on its own if you've got some). Foam on its own isn't good unless its fairly heat resistant, though a couple of sheets of kitchen towel on top of it may give you enough soldering time before it melts. Otherwise try a silicone mat. The board may be self-supporting, it may need chocking up if there are no tall components on one side, or you may need to go whole hog and use a PCB vice.
I've never liked using Plasticine, BlueTak or similar as it tends to leave a deposit on a heated connector pin which can be a PITA to clean off. OTOH it can be helpful on the track side to retain the parts while you flip the board over, as long as you remove it all before soldering, or for box headers, where it never has to touch any pins.
If you've got a lot of bare headers to insert that must be properly aligned and vertical, *DON'T* use a solderless breadboard you care about as a jig - the solder dross and hot pins will destroy it. Ideally tape a few spare boards together and use them to hold all the headers so you can simply drop the board you are working on over them and solder all the pins in one pass. If you don't have spare boards, but the pins are on a 0.1" grid, use a few layers of plain perfboard.
'Helping hands' aren't much use for larger boards unless you've got the luxury of a tilt-able PCB vice or can get the board well up off the bench e.g with opposite edges on a stack of phonebooks, so there's space for the helping hands to hold the part. For very small boards, if you can rig an extra arm lower down so you've got three clips, two holding the board by opposite edges and one holding the part up can work nicely