How to solder connections to this board
Those are test-points, in your example gold plated ones, and are not intended to be used to solder wires onto them.

Normally they are used with a bed-of-nails using spring loaded pogo-pins to make contact to the circuit using testing equipment. Pogo-pins come with a variety of tips for contacting with various features on the board.




Note the use of the large pointed pins in the above image that go through the mounting holes in the board that act to align the board with the pins. The big fat ones are keyed to the edge of the board to get it aligned close to the smaller ones that go through the holes.

The alignment pins are longer than the pogo-pins so the board is in the correct position before they make contact.

Sometimes double sided, "suitcase", fixtures are used...