Cornerstone: Tinkers' Construct - Getting Started

The first thing you are going to want to build is a Smeltery, which can be used to double your ores, create alloys, and cast tool parts.  You can also skip right over the diamond requirement by casting obsidian blocks right in the smeltery, just combine 1 part lava and 1 part water!  Solid materials like ores and stone can be inserted into the Smeltery Controller, while liquids should be poured into a drain.  You can pour from a bucket, reservoir, or place a faucet over a drain.

Start off by collecting a stack or so of Clay, Gravel and Sand.  Combine to make Grout, then cook the Grout in a Furnace to make seared bricks.  Use the bricks to make a Seared Tank, Smeltery Controller, at least one Drain and one Faucet, a Casting basin and a Casting table.  Turn the rest of the bricks into blocks, then build a 3x3x1 multi-block structure including a drain, Smeltery Controller, and Seared Tank on any side.  Attach a faucet to the drain, then place up to 4 buckets of lava in the Tank.  You can also pipe lava into the tank using Hardened Fluiducts from Thermal Dynamics.

The Casting Basin can hold 9 ingots (in block form) of metals.  You'll need a Casting Table and an Ingot Cast in order to drain single ingots at a time, otherwise make sure to input metals in multiples of 9 and use your casting basin.  Casts are created by pouring 1 ingot of Aluminum Brass or 2 ingots of gold over a tool part that has been placed in the Casting Table; be warned this will consume the part so use cheap materials like a clay brick for an ingot and stone tool parts.  You can always drain any extra molten liquid into a Seared Tank, if you have too much and want to keep the material.  To drain from a Seared Tank back into the Smeltery, place the tank next to a drain, place a faucet on the tank so it is over the drain, and use the faucet and it should pour molten liquid right back into the Smeltery for use again.

You can melt different materials at a time, however be warned that some materials combine to make an alloy.  Some common alloys:

3 ingots Aluminum + 1 ingot copper = 4 ingots Aluminum Brass
3 ingots Copper + 1 ingot Tin = 4 ingots Bronze
1 bucket Lava + 1 bucket Water = 1 block of Obsidian
1 ingot Gold + 1 ingot Silver = 2 ingots Electrum
3 ingots Tin + 1 ingot Silver + 1 block of Glowstone = 4 ingots Lumium
3 ingots Copper + 1 ingot Silver + 4 pieces of Redstone = 4 ingots Signalum
3 ingots Lead + 1 ingot Platinum + 4 Ender Pearls = 4 ingots Enderium

There are many more, look up "Molten" in JEI/NEI to see their components.  Some math may be required to translate mB into ingots or blocks.

You can upgrade the Smeltery by increasing the size of the multi-block structure, but you don't need to make seared bricks with Grout!  Put cobblestone directly into the Smeltery and pour into casting basins and use the seared stone blocks to build the Smeltery even larger.  Seared Stone can be cast into ingots to form individual bricks if necessary.