We will be using the research rules from Space: 1889. Characters will have 1 general research die (d6) per point of Intelligence (d8 Intelligence = 8 research d6) and 1 die per 2 points of skill (Physics d8 = 4 research d6). Increasing skill levels will add research dice, and additional dice can be earned through roleplay or can be bought for 4 Advancement points.

Here's a longer, more detailed explanation from when I was explaining it to my players:
Research and Inventing
Okay, the rules use a pool of d6. You get one d6 for every point of Intelligence (d6 Intelligence is six d6, d8 Intelligence is eight d6) plus one d6 for every STEP of skill. So Physics d8 gives you four d6, Electricity d8 gives you another four d6.

So, 8d6 for Intelligence, 4d6 for Physics, 4d6 for Electricity gives you 16d6 in your pool of Research Dice. Once dice are rolled, they are lost from your research pool. You can buy more dice from advancement points, and you get more when you raise skills or from examining other inventors' work.

Inventions have a research level and an experimental number. For example:
Hand lamp (research 3, experiment -3)
Battery (5, -3)
Electric motor (10, -1)
Long wire power (15, 2)
Electric rail gun (22, 2)

The research level is how skilled you have to be to invent that device, the experiment number is how hard it is to make one.

So, Kevin's inventor wants to make a railgun. He needs a research level of 22 or better. He takes 5d6 from his pool and rolls and gets 5+2+2+5+6=20, not enough. He rolls another d6 and gets a 5, +20=25. His research level is now high enough to build the railgun, but he only has 10d6 left in his research pool. Your research level is permanent, it can be added to, but it does not get rerolled or lost.

Now he rolls 1d6 to make the railgun. He needs to roll better than a 2 and gets a 1. The experiment is a failure and that die is lost. He has 9d6 left. He tries again and gets a 3. He has succesfully invented a railgun and has 8d6 left. The reliability or power of an invention is equal to your die roll minus the experimental number. So 3-2=1, the railgun has a reliability of 1. Kevin decides that's pretty poor and rolls to improve his invention. He now has to roll better than the device's current reliability, NOT the experiment number. It is easier to improve an existing invention than it is to make it in the first place. He spends another research die and rolls a 2. 2 is better than 1, so the railgun now has a reliability of 2 and he has 6d6 left. That's still pretty sad. Kevin spends another research die and rolls a 5. He has 5d6 left in his research pool, but now the railgun has a value of 5. Some inventions may also have a cost for raw materials and you also need the appropriate laboratory equipment.

So, Kevin's character has a research level of 25 and only 5d6 left in his research pool. During the campaign, the party captures a lightning cannon from an opponent. Kevin's inventor examines it and must roll Intelligence d8 plus his Electricity d8 to understand the device. He succeeds and he is rewarded with an extra research die. He now has 6d6 in his pool. Kevin rolls 1d6 and gets a 5, raising his research level to 30, but he is back down to 5d6 in his research pool. He may now invent energy cells (25, 5) and a lightning cannon (28, 4). Kevin spends advancement points and raises his Electricity skill level to d10 and gets another research die as well, bringing his pool back up to 6d6.

Kevin decides to invent batteries (5,-3) and and electric motor (10, -1) to use in an electric carriage. He spends one research die on the batteries and rolls a 4. 4 minus -3 is 7, so the batteries have a reliability of 7. He rolls another research die and gets a 2, 2 minus -1 is 3, the motor has a reliability of 3 and Kevin has 4d6 left in his research pool. His research pool is dropping, so Kevin decides to buy more research dice with advancement points. A research die costs 4 advancement points, Kevin spends 8 points for 2 more dice, raising his pool to 6d6 ("Have you read Tesla's latest treatise on electromagnetism? Fascinating work!").

I am also going to allow people to improve existing items. Lets say you have Machinist and Naval Architecture. You could improve the rate of fire or the range of an existing cannon.