It looks like this question has been asked several times by several different people. Most of our answers have been fairly vague and general (e.g. "look at released exams" and "do more practice"), so I thought I would write up a more thorough answer based on what I've seen so far during the season. If you are comfortable with circuit theory, preparing for the lab portion should take no more than a couple hours of practice spread across a couple of days.
First and foremost, the biggest weakness I've seen at invitationals is a general unfamiliarity with how breadboards and multimeters work. You are almost guaranteed to see these two items appear at almost any competition, so the first step is to acquire these items to begin practicing with them. I personally dislike electronics kits since they provide very low-quality components, but in the interest of keeping costs low, I have linked to a kit that I think would work well for practice. The items you should focus on in the kit are the breadboard, jumper wires, resistors, potentiometer, and LEDs. The rest of the stuff is superfluous. I should also point out that most schools have many of the aforementioned components in the physics section of their storage closet, so it doesn't hurt to ask your science/physics teachers first.
Beginner Electronics Kit
For the multimeter, I have linked in the one used at the MIT Invite. It's very inexpensive and is certainly not a top quality meter, but I think for the purposes of Science Olympiad, it's probably better to be more familiar with a low-quality meter since that is what you are likely to find at competitions. That being said, it definitely has more than enough functionality for what you will need at competition. You can also ask your physics department if they could lend you one, but I think it would be good for SciOly to buy one yourself and bring it to competition (see one of my earlier posts regarding bringing your own meter).
Multimeter
Now that you've got your materials, probably the single most important thing you can do is get comfortable with how to use a breadboard. This doesn't mean look it up the night before and hope to figure it out on competition day. Using a breadboard takes a bit of practice, but once you've got the hang of it, it's really easy to use and should feel like second nature. Begin by making simple series and parallel circuits with your resistors and jumper wires. I would recommend the small pre-bent wires in the kit over the super long flexible wires since it makes for neater circuits and helps you develop the ability to read-off the circuits directly off the breadboard. Good breadboarding is a skill that comes with practice. After this, build up to making larger circuits.
Part 1, Problem 3 of the lab section of the MIT Invite is an example of a more complex circuit on a breadboard that does not use series and parallel connections. There is a breadboard diagram included in the released exams as well as a schematic, so that can serve as practice. Once you figure out how to make series and parallel connections, you are well on your way to building most circuits you are likely to encounter.
After you can build and interpret breadboard circuits, you should get comfortable with making measurements. The first two measurements you should go for are voltage and resistance since there is a minimal chance of damaging your meter. Current measurements are more risky. Read up on how to do those properly (i.e. you almost always will have to open up the circuit and put your meter in series -- never put your meter in parallel by just poking the live circuit directly with the probes ). Ask someone if you are unsure. Resistance measurements can be made passively with the meter so try making some resistance measurements of your series and parallel circuits to see if the numbers match your theoretical values (remember most resistors you find have a 5% tolerance). Voltage measurements require you to apply some voltage across your circuit (i.e. power it on) before you measure anything. This was a common mistake I saw at tournaments which was that competitors were trying to use the voltmeter on a disconnected circuit. The kit I linked in above comes with a nice breadboard power supply that you can plug in, and it will power on the rails with 5 volts. Alternatively, you can use normal AA or AAA batteries to supply 1.5V or 3 V to your circuit. You can also try measuring the voltages of the batteries directly with your meter too. What happens when you flip the measurement you make by flipping the red and black leads? I saw this confuse several teams.
If you've gotten this far in your practice and you are truly comfortable with the two skills above, then you should be able to figure out where to go from here and what other skills you personally need to develop. Some other things to think about practicing include using LEDs in your circuits, possibly including an op-amp in your circuits (Div C), doing power calculations using voltage measurements, reading resistor values, and using a potentiometer. But even just completing the two paragraphs above will go a long way towards increasing your competitiveness in the lab section.
Some other random thoughts pertaining to the lab from observations of common problems during competition:
- LEDs are polarized. The positive side has the longer leg, but the more reliable way of determining this is to look at the cap of the LED. There should be a flat edge on the side of the negative lead. This is useful if the legs have been cut short. LEDs (and diodes in general) also do not have a single resistance value. They have a forward voltage drop. Understand what this means.
- A resistor in series with a component will allow you to make a current measurement using only a voltage measurement if you know the value of the resistor.
- Understand how to set up a multimeter to the right setting. You may be asked to pick the right setting and plug in the probes to the right sockets.
- Know how to read resistors! Spend a couple minutes to just practice this. I can't emphasize enough how many teams wasted time figuring out how color codes work during the competition rather than taking 10 minutes before the tournament to look at this. Memorizing is ideal but totally not necessary given that you have a binder. If you are trying to memorize, note that most of the colors follow the order of the rainbow, so the order goes Black, Brown, ROY G BV, Gray, White (missing Indigo). Also, the chart might be worthwhile to print out in color.
The usual advice of practicing with your partner and looking at old exams is of course very important, but hopefully this helps people get started in general.