Here's the first article of the Remonstrants:
ARTICLE I. That God, by an eternal, unchangeable purpose in Jesus Christ, his Son, before the foundation of the world, hath determined, out of the fallen, sinful race of men, to save in Christ, for Christ's sake, and through Christ, those who, through the grace of the Holy Ghost, shall believe on this his Son Jesus, and shall persevere in this faith and obedience of faith, through this grace, even to the end; and, on the other hand, to leave the incorrigible and unbelieving in sin and under wrath, and to condemn them as alienate from Christ, according to the word of the Gospel in John iii. 36: "He that believeth on the Son hath everlasting life; and he that believeth not the Son shall not see life; but the wrath of God abideth on him," and according to other passages of Scripture also.
The first thing to note here is that God is choosing to save out of the fallen & sinful race. This distinguishes Arminianism from supra-lapsarianism, as they see election from pre-fallen and uncreated mankind. This aspect however, does not distinguish Arminianism from sub-lapsarian Calvinists.
The second point of note is the condition of faith. This is different that sub-lapsarian Calvinists as well who do not think that God contemplated man as in faith when He elected them. Hence, for them, faith is not a condition for election. But for Arminians faith is a condition for election.
Now how does this work exactly? There are three primary Arminian views of election/predestination.
1) based on foreseen future faith
2) Corporate election
3) Middle knowledge of faith
The first view is that God looks down the corridors of time, sees who believe and chooses to save them. This view has been criticised as somewhat of a rubberstamp, because if God sees their faith as already future, His choice doesn't change that.
The second view is that God chooses to save the category of believers. Christ is the ship, who's destination is heaven and God chooses to save anyone on the ship, but no one has to be on the ship. In this view, no individual person is chosen.
The third view is God chooses to save those who He knows would believe under a circumstance of God's choosing. God know how people would choose under different circumstances, chooses one circumstance and as a consequence chooses certain people. This is the view that I hold to. It was made popular by Molina, and arguably it was Arminius' view. Here's an discussion of Arminius on that point:
Any of these three positions above fall under conditional election or Arminianism. They are at variance with the Calvinist tenet, unconditional election.