Figurine - Explosives: Sealed cistern [WKML broadcasting station]
Effects: Explosives skill raised by 10 points.
Additional info: I assume that you may have a lot of problems locating the cistern. Ignore the main building of the broadcasting station and proceed south. Head down the cliff and find a grate leading to the cistern (screen). The figurine can be found inside, next to a body and a large radio.
Figurine - Medicine: Clinic [Vault 101]
Effects: Medicine skill raised by 10 points.
Additional info: I would strongly recommend collecting this figurine at the beginning of the game, because after dealing with two initial tutorial segments you'll find yourself standing next to it. If you miss it somehow, you can take it later when you decide to return to Vault 101.
Figurine - Repair: Evan King's house [Arefu]
Effects: Repair skill raised by 10 points.
Additional info: The situation here is similar to Lucas Simms's house from Megaton. The most important thing is that you focus only on taking the figurine, because otherwise Evan may think of you as a thief.
Figurine - Science: Living quarters [Vault 106]
Effects: Science skill raised by 10 points.
Additional info: Once you've reached Vault 106 - entrance you have to use the terminal to unlock access to the living quarters. Ignore strange visions while exploring the crypt, but watch out for inhabitants of the vault.
Figurine - Lockpicking: Eastern Bethesda offices [Bethesda ruins]
Effects: Lockpicking skill raised by 10 points.
Additional info: Don't go to the western building my mistake, because it's more exposed and you'll probably arrive there in the first place. There are a lot of raiders outside the building and the structure itself is being protected by a few turrets.
Figurine - Perception: Museum of Dave [The Republic of Dave]
Effects: Perception raised by 1 point.
Additional info: I would recommend that you synchronize taking the figurine with perform a miniquest for Dave.
Figurine - Speech: Eulogy's quarters [Paradise Falls]
Effects: Speech skill raised by 10 points.
Additional info: In order to acquire this figurine you must first gain access to the inner compound of Paradise Falls. This probably means you'll have to perform a task for Grouse. You can also kill the slavers if you're a good person. If you're a bad character, you'll have an easier entry (without completing any quests). The figurine can be found in the main room of Eulogy's quarters.