Interpretation of the Question
The question asks how the G-protein α- and βγ-subunits move, but does not state the context or circumstances of the movement. I assume that the question is, in fact:
How do the G-protein α- and βγ-subunits move apart and migrate
from receptor to target enzyme when their interaction is prevented by
the binding of GTP to the α-subunit?
False premise in the question
The problem envisaged in the question is that as the α- and γ-subunits have lipid moieties covalently bound to their amino acid chains, they are somehow part of the lipid cell membrane. This non sequitur may arise from a misunderstanding of lipid chemistry: the cell membrane is a bilayer the main constituent of which is individual molecules of phopholipids containing two long fatty acid chains and one polar organic phosphate (e.g. phosphatidyl choline) attached to a glycerol backbone. Other hydrophobic molecules (cholesterol, proteins with hydrophobic amino acids on their surfaces) can interact with these phospholipids.
The lipid moieties attached to the G-protein subunits are, in contrast, single palmitoyl or myristoyl fatty acid chains (in the case of the α-subunit) or farnesyl or geranyl (substituted fatty acid) chains (in the case of the γ-subunit). So the idea that they are somehow equivalent to the membrane phospholipids is incorrect.
How do they move?
As the lipid bilayer is fluid, its constituents can move within it, like ships on the sea. A review by Wedegaertner discussing G-protein trafficking illustrates this as shown below:
When the interaction between the subunits is prevented by GTP, they are free to drift apart in the membrane, like a boat cut loose from a ship at sea. The illustration shows them attached to the membrane by a single line representing the lipid group, but also considers evidence that they may move away from the membrane, presumably because the interaction is weakened on dissociation. Their movement is presumably random thermal motion in each case, as is that which leads to their reassociation after the GTP is hydrolysed.
However, as @BryanKrause mentions in his comment, it should be emphasized that the ability of the subunits to ‘float’ through the membrane (rather than ‘sink’ into the cytoplasm) facilitates their mode of action. They must first associate with the hormone/agonist receptor to receive the initial signal (or first messenger) and then move to interact with the target enzyme/protein which transmits the signal within the cell (e.g. through the second messenger cyclic AMP produced by the enzyme adenyl cyclase). See, for example, this Nature Scitable article.
