This is just a short demonstration on how to assemble miniature models. I'm going to show this on a "Vampire Counts Necromancer"-Figure, but most of these steps can be used for any kind of model, be it a hero, monster, vehicle and so on.

This primer is aimed towards beginners; people who have no or very little experience in modelling. Most of these steps will seem pretty obvious, but are easy to miss if you have never been told.

Building Miniatures is very simple. Ally you need is a few basic tools and some patience. Basic reading skills don't hurt either...

So let's get going.

Step 1: You Will Need:

To start you will need the following:

Hobby knife: Not really necessary, but can be used to substitute the following two tools. Otherwise only to open the box
Model Cutters: You can use normal cutters, just make sure they are thin enough to fit between model and sprue without damaging the model. If you don't have model cutters, you can use a hobby knife (careful - fingers), but you might have to do more cleanup than with cutters
Scraping Tool: This will be used for scraping off mold-lines and sprue-residue. It's basically just a piece of straight metal. Again, if you don't have those, you can use your hobby knife (again: careful - fingers).
Glue: Superglue and/or plastic-glue. If you're new to the hobby or just want to try it out, just get superglue; it will work fine (more later). Also, get the cheap stuff from the dollar-store, it's just as good as the expensive ones.
Cutting Mat: Not really necessary, but it doesn't hurt to put down some protection.

Obviously you will also need a model. If you're just starting with miniatures there are two ways you can go with this:

Get the cheapest model you can get. If you screw it up or don't like doing this, at least you didn't waste a lot of money. Problem here is, that sometimes cheap models are crooked or bent and don't fit together very well, so they can be very frustrating to a beginner.
Get a box of several similar models. This way is a bit more expensive, but if you screw up one model you have more to practice. Also, once you get to painting, you have several similar models to practice.

Be sure to check the difficulty-level on the box or ask the staff about how difficult the model is. You don't want to start on a Master-Level as your first try; these things are tough. Get something nice and easy, ideally something that is aimed towards kids or younger people. These may lack some of the excessive details of the higher-tier models, but they are more satisfying to build, especially if you're just starting out.

Step 2: Let Them Free...

Now it's time to get close and personal with your model.

Get your hobby-knife (or a pair of scissors) and open the box. Be careful not to damage the model while cutting.

Some boxes (like this single-sprue model) can be quite nasty to open. Watch your fingers!! Others come in cardboard-boxes wrapped in plastic. Usually you can get those open with your fingernails. When your model is free, have a look at the instructions. Yes, i know, manuals are for the weak. But in this case, "the weak" will end up with the nicer looking models.

You notice the numbers next to the parts on the assembly leaflet. These numbers are there for a reason. If you deviate from this sequence your model might end up with his head on his butt or have large gaps, because the parts might not fit correctly.

You can skip this step if you have bought a pre-assembled model. The next step however is not optional.

Step 3: Cut and Scrape

Next we cut the model from the sprue. Again, there are two ways to do this:

Cut only the part you need for the next step. This will keep you nice and organized. However, it will mean, that you will have to check out every single piece you cut out for mold-lines and plastic residue, and this can be quite tedious.
Cut out all parts at once. This may be a bit more chaotic, but in my mind the better alternative. If you collect the pieces in the empty box, you'll make sure not to lose any. Also, once you cut out all pieces, you can then remove all mold-lines at once and all residue at once. This way you will make sure not to miss any. However, if your model contains lots of parts, you might spend a lot of time looking for that one small piece you know you just had...

To cut the model from the sprue, place the cutter with the flat side to the model and carefully snip the plastic. If there is not enough room, try cutting away a part of the sprue to get better access.

If you have to use your knife for cutting the parts, make sure to cut down onto the cutting mat. DO NOT cut towards you or while holding the sprue in your hand. You can (and will) seriously hurt yourself.

You should also never try to force the cutter into a tight spot, as this may bend (or even break) parts the model.

As soon as all parts are cut out, take your scraper and look for plastic bits where you cut the model from the sprue. These will have to go.
You can try to get at them with the cutters, now that you have a better angle at them. Otherwise run the scraper with gentle pressure over these parts, until it's smooth.
If the bumps are too big, try to cut bits of them away with your knife. Be careful not to accidentally carve out a chunk of plastic while doing this.

If you have to use the knife, always scrape away from you.

Next, look for mold-lines. These are thin lines left over from the casting-process running along the whole model between the plastic sprue-bits you cut off earlier. Sometimes they are so thin you hardly see them. You will still need to scrape them off, otherwise paint may catch on them and leave ugly spots when painting.

To scrape off mold-lines, just run the scraper gently over them, until you can't see them anymore. You can check with your fingernail if it's still there.

When removing mold-lines, make sure you don't press the scraper down so hard, you take off the details of the model.

Once you have removed all the mold-lines and plastic-bits it's time to glue.

Step 4: Don't Glue Your Fingers Together...

Now to finally assemble the model. Lay out your parts in front of you and glue them together.

Simple, right?

Well, not quite. There are some things to be considered.

If your model is made from metal (like pewter or so called "white metal") or resin (sometimes called "finecast"), you have to use superglue. Plastic-glue won't work on these materials. You could try PVA or white-glue, but superglue is your best bet. Be careful though not to use too much, as this can leave a chalky residue on the model (which is easy to scrape off, but annoying). The upside with superglue is, there are several ways to break the glue-bond without damaging the model.

If you happen to get superglue on your fingers, dip them in water. This will instantly set the superglue and make it much easier to peel of later.

If you have a (normal) plastic model, another option is the use of plastic-glue. Although it's often called glue, it's actually a bonding-agent (or cement) for plastic. It works by slightly melting the plastic parts and - on contact with each other - bonding them together. This creates a much stronger bond, as you end up with one single piece of plastic.
There is however a downside to using plastic-glue. Because it melts the plastic, it's possible to accidentally melt away details on the model. Also, if you later decide to re-pose the model, there is no way to break the bond short of breaking the model apart.
If you should get some on your fingers don't touch the model until you have wiped you fingers. Otherwise you might melt your fingerprint into the model (which looks ugly)

When you are ready, take part one and two and dry-fit them before applying glue, just to see how they align. Then take a small drop of glue (you really don't need much), apply it to one of the pieces and bring the two pieces together. Hold them like this for a few seconds. If the glue-joints are very small you might need to hold them quite a while. Make sure to push them together as tight as possible so you don't get any large seams or gaps.
Keep doing this until your model is completely build.

We're nearly done now.

Step 5: Final Cleanup

On this picture you can see a slight gap between the two shoulder-pieces of the cloak. To remove this, just run your scraper along the seam until you can't feel it anymore. It's OK if it's still visible, it will be covered up with paint, as long as it's smooth.

Congratulations, your model is completely built and ready for priming (nope, not yet ready to paint). But this we will do another day...