Migrants should come automatically every spring and fall, sometimes in the summer too. However, there are some things you may have done to scare them off; essentially, your fortress has a reputation as a worthless poverty-stricken hole in the ground, so no one wants to move there. The formulas the game uses to determine migrant behavior aren't completely known, but there are some rules of thumb.
The biggest is to make sure you are trading pretty heavily with the dwarven caravan. This is how news of your fortress reaches the rest of the dwarven civilization. If the caravan goes home unsatisfied, then the people of your civilization feel there's nothing worth having at your fortress. Worse, if the caravan doesn't go home at all, then people will feel your fortress is too dangerous. If this happens a lot, instead of the "There were no new migrants this season" message, the game will eventually give you a message like "No one was willing to migrate to such a cursed deathtrap this season." This is a sign that you should maybe stop killing dwarven caravans (killing humans and elves is still fine).
SevenSidedDie also has a good point in the comments. A lot of new players tend to change their configuration settings to avoid some of the more difficult parts of the game, and one of the first things they usually change is the population cap, to 70. This prevents goblin sieges from arriving, because they require 80 dwarves. If you're using some packaged download such as the Newbie Pack, the mod creator may already have done this for you.
To address your other problems, even relatively untrained soldiers should be able to stand against normal goblins if they have good armor (avoid goblin lashers and goblin bowmen, they are much more dangerous). Make sure all your soldiers have full armor, preferably steel. At a minimum, helmets, breastplates, greaves, and shields are all worthwhile. Gloves and boots are less important but still useful. Traps are good too, but a lot of people think they're cheap (because they're honestly too good).