What physical force attracts the anti-codon on tRNA to the codon on mRNA during translation? I know that these two bond together, but what actually makes the tRNA move through the cytoplasm to the mRNA on the ribosome?
As with many processes in cellular biology, nothing really moves anywhere, attracted by specific force. What that means, is that any molecule has a chance to interact with any other molecule, say, bind to it. Only force that is acted is electrical force of attraction of negative charges to positive ones.
Due to diffusion and temperature fluctuations, molecules wander around, bumping in each other. Sometimes, two complimentary molecules will bump into each other in a very desirable, energy-efficient orientation. Their atomic-scale interfaces (with tiny charges on it) will find each other as neat as hand finds glove of the right size/orientation neat and comfy. That is the way, for example, tRNA finds slot on ribosome/mRNA complex to plug into. just simple key-and-lock, or hand-and-glove model, that's all there is. And beauty is that you can try computationally calculate probability and energy of different interactions from molecular 3D structures.
Now, there are many tRNAs, but Glycine-tRNA will bind tightest to glycine-codon/ribosome complex. There is a chance that Alanine-tRNA will get in that spot, but that chance is very little compared to chance of proper interaction. Also, because interfaces of Ala-tRNA and Ala-codone don't match exactly, molecular vibration due to heat (temperature) will destroy this complex quickly. This allows specificity.
I wanted to illustrate the process I explained in a comment on aandreev's answer with some images, I just copy/pasted the actual text sections, however.
The tRNA is bound to an elongation EF-Tu (which is also bound to GTP). The Ef-Tu has an affinity for a factor binding site in the A-site of the large ribosomal subunit. You have an anticodon triplet on the tRNA, and a bend in the 3D structure of the anticodon loop gives you wobble base pairing on the last nitrogenous base. When the anticodon of the tRNA binds tightly enough to the mRNA, two adjacent adenines in the 16s rRNA of the A site crosslink (via hydrogen bonding) the minor grooves formed by the correctly paired tRNA. These adenines don't differentiate between G:C or A:T pairs, just the tightness/correctness of the tRNA binding.
In short, electrostatic forces and mechanical forces. Electrostatic forces are responsible for the classic Watson and Crick base pairing that is de facto what brings together codons and anticodons. Mechanical forces are involved in the displacement of the pairing and the shift of the RNAs. The ribosome's subunits literally grab and move both messenger and tRNAs.