A laser beam nominally has a power density cross-section which is Gaussian, so there is more power in the middle of the beam and less at the edges. When the beam strikes a translucent object (microns in size) overall the refraction of the beam tends to be away from the centre of the beam. Each emitted photon has a very small momentum, but non-zero. Thus, due to the law of conservation of momentum, the translucent object is forced away from the photons. That is towards the centre of the beam.
Once an object is gripped by the beam, it can be moved around by steering the beam. It is also possible to induce spin.
A typical setup has only one or two laser beams. More complex operations require many, even dozens, of beams. A recent development is of holographic tweezers where one beam is split into many individually controllable beams using a 2D-array of switchable optical phase delay elements which form a controllable / programmable holgraphic plate.