In the first round of betting, the betting would be capped at 5 bets/raises, meaning once the bet reached $5 no one could raise any further. So the most that any one bettor could put in the pot during that entire round would be $5, and the most that could be in the pot at that time would be $25. That's the preflop round.
The flop betting round would once again begin with a bet of $1 (supposing someone opened the bet, rather everyone checking). If no one raised and everyone called, then the bet would stay at $1, everyone would put in $1, and the pot would be at $30. If instead one person raised and everyone called, then the bet would be $2, everyone would put in $2, and the pot would be at $35. And if instead everyone raised then the bet would be $5, everyone would put in $5, and the pot would be at $50.
The turn and river would work the same as the flop, except that the betting would start at $2 and each raise would be another $2.
With the betting capped at five bets in each round, then the most each player could put in the pot would be $5 + $5 + $10 + $10 = $30 for the hand, making a $150 pot. This never happens. But it is the theoretical maximum that any one player could lose ($30 in one hand) and the maximum that any one player could win ($150 in one hand). Typical hands might see a bet and a raise preflop, a bet on the flop and turn, and a bet and raise on the river for a total of $9 put in the pot by any one player.
Typical buy-ins for a fixed limit game are anywhere from 10 to 50 big bets. In a $1/$2 limit game, that would be $20 to $100. If that seems too large for your players, consider playing smaller stakes. However, note that a single buy-in lasts much, much longer in a limit game than in a no-limit game. You never have to place your entire stack in jeopardy on a single hand; you just lose it a little bit at a time. So if your players are used to going bust and rebuying over and over in a night of NL, then when they switch to fixed limit they can probably afford to have larger buy-ins and higher stakes.